Download - Home Test 3
-
MA , 3, 001
1. c x dx6x
2 567
2. c 13(x2 + 6x 1)
(x + 7)(x2 + 8x + 20)dx .
3. c 2 + 3xx 2 + 1 dx .
4. c 0
12
sin6x
cos26x 36dx
5. c 0
14
(x2 5x 1) sin7x dx .
6. c 0
12
sin24x dx .
7. c cc 215
5dx
(x 4) ln5(x 4)
.
8. c , y = 4x2 + 9x 12,
y = 5x2 . .
9. c , c Ox ,
y = x2 + 7x y = 0 x [ 8, 7] .10. R(x), x
MR = x8 360 .
. 1 300 2012/2013 .
-
MA , 3, 002
1. c dx(3 + 4x)95 .
2. c 18(x2 + x 9)
x3 + 3x2 18xdx .
3. c x + 9 2
x + 18dx .
4. c e78
e2
8dx
x ln28x.
5. c 13
13 3
arctg3x dx .
6. c 0
15
sin25x dx .
7. c cc 7
1dx
(x + 8) ln(x + 8)
.
8. c , yx = 63, x + y = 16 .
.
9. c , c Ox ,
y =9
x 6, x = 2 x = 3 .
10. e
z(t) = 36t 5 . 06t2 , t ( ), .
C 7 . 57
, 70 .
. 2 300 2012/2013 .
-
MA , 3, 003
1. c x dx5x
2 635
2. c 3x2 3x 12
3x2 x3dx .
3. c x 8x + 7 1 dx .
4. c 18
116
4 ctg24x + 2 ctg4x 1
sin24xdx .
5. c 13
13 3
arctg3x dx .
6. c 0
2
cos6x sin7x dx .
7. c cc 1
+
23x1 dx
.
8. c , yx = 7, x + y = 8 .
.
9. c , c Ox ,
y =6
x + 4, x = 8 x = 6 .
10. ()
8 20
f (t) = 3000 + 77t 3t2, t , 8 t 20.
, 13 15 ,
1 5 . .
. 3 300 2012/2013 .
-
MA , 3, 004
1. c dx(1 2x)45 .
2. c 53(x2 5x + 7)
(x + 5)(x2 4x + 8)dx .
3. c x 7x 2 3 dx .
4. c e5
9
e1
9dx
x ln49x.
5. c 0
12
arctg2x dx .
6. c 0
2
cos2x sin7x dx .
7. c cc
4
sin2x dx
.
8. c , x + y = 5, yx = 6 .
.
9. c , c Ox ,
y = x2 x y = 0 x [ 4, 3] .
10. ,
: z(t) = 0 . 376t2 + 3 . 1t + 8 . 3 t
( ), .
. 4 300 2012/2013 .
-
MA , 3, 005
1. c 14x + 37x
2 + 3x + 63dx .
2. c 15(x2 6x 3)
(x 6)(x 7)(x 1)dx .
3. c x 4x + 1 2 dx .
4. c ln3
ln2e2x
49 81e4xdx .
5. c 0
10
(x2 x 4) cos5x dx .
6. c 0
2
cos3x sin7x dx .
7. c cc 2
3x 8 7 3 x
3 xdx
.
8. c , yx = 5, x + y = 6 .
.
9. c , c Ox ,
y =8
x + 9, x = 0 x = 9 .
10. K(t),
( , )
I(t) = 390 t58 , ( t = 0) 170 .
. 5 300 2012/2013 .
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MA , 3, 006
1. c dx(1 + x2) arctg5x9
.
2. c 20(x2 + 3x 5)
(x 4)(x2 + 4)dx .
3. c x + 2 + 1
x 7dx .
4. c 0
14
cos7x
sin27x + 4dx
5. c 0
12
3
arctg2x dx .
6. c 0
18
cos26x dx .
7. c cc 1
36 + 7 3 x
3 xdx
.
8. c , y = 3x2,
y = 2x2 3x 2 . .
9. c , c Ox ,
y =1
x + 5, x = 1 x = 2 .
10. q TC(q),
q
MC = e3.2q, 58 .
. 6 300 2012/2013 .
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MA , 3, 007
1. c dx2x 6 .
2. c 2x2 + 12x + 14
(x + 4)2(x + 2)dx .
3. c x 2x + 5 + 1 dx .
4. c ln2
ln3e2x
e4x 7dx .
5. c 0
12
(x2 5x + 2) sin6x dx .
6. c 0
2
sin4x sin3x dx .
7. c cc
1
85x2 dx
.
8. c , y = x2 + 2x + 4,
y = 2x2 + 4x + 12 . .
9. c , c Ox ,
y = x2 4 y = 0 x [2, 3] .
10.
e t (t )
V(t) = 77 + 7 cos
6(t + 7)
. .
. 7 300 2012/2013 .
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MA , 3, 008
1. c x 3x2 578 dx .
2. c 17(x2 + 3x + 4)
(x + 3)(x2 + 4x + 20)dx .
3. c x 8 + 1
x + 17dx .
4. c 118
124
ctg6x dx .
5. c 0
14
(x2 + 4x + 5) sin7x dx .
6. c 0
18
cos26x dx .
7. c cc 0
e2xdx
.
8. c , yx = 3, x + y = 4 .
.
9. c , c Ox ,
y = x2 + 3x y = 0 x [0, 3] .
10. V(t) ,
, 23% , . .
t V
V= 0 . 23t .
12 , , V(0) = 52 .
. 8 300 2012/2013 .
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MA , 3, 009
1. c 4x + 52x
2 + 5x 313
dx .
2. c 29(x2 3x + 7)
(x 5)(x2 + 4)dx .
3. c 1 + xx 4 2 dx .
4. c 34
78
3 ctg32x + ctg2x + 1
sin22xdx .
5. c 0
4
(x2 + 3x 3) cos2x dx .
6. c 0
28
sin27x dx .
7. c cc e79
e9
9dx
x 7 + ln9x
.
8. c , x + y = 9, yx = 14 .
.
9. c , c Ox ,
y =1
x 2, x = 8 x = 0 .
10. ,
: z(t) = 1 . 095t2 + 9 . 7t + 6 . 9 t
( ), .
. 9 300 2012/2013 .
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MA , 3, 010
1. c 4x 32x
2 3x + 278
dx .
2. c 2x2 + 4x 16
(x 1)(x2 6x + 9)dx .
3. c 9 + x 6
x 2dx .
4. c e78
e4
8dx
x ln28x.
5. c 0
13 3
arctg3x dx .
6. c 0
2
cos6x sin3x dx .
7. c cc 5
9x + 4 x 5
x 5dx
.
8. c , y =4
x2 + 8, y =
1
12x2 .
.
9. c , c Ox ,
y =9
x + 8, x = 3 x = 7 .
10. q TC(q),
q
MC = e1.4q, 45 .
. 10 300 2012/2013 .
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MA , 3, 011
1. c dx(3x + 5)106 .
2. c x2 + 4x 6
x3 2x2 + xdx .
3. c x + 3 4
x + 12dx .
4. c ln5
ln6e2x
e4x + 25dx .
5. c 13
13 3
arctg3x dx .
6. c 0
2
cos5x sin4x dx .
7. c cc 1
5x + 2 4 5 x
5 xdx
.
8. c , y =36
x2 + 216,
y =1
252x2 . .
9. c , c Ox ,
y = x2 + 6x y = 0 x [0, 1] .
10.
MC(x) = 92 4x 5x2, 82 .
.
. 11 300 2012/2013 .
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MA , 3, 012
1. c dx4x + 5 .
2. c 2x2 14x + 16
(x 2)(x2 6x + 8)dx .
3. c x 4 + 8
x 20dx .
4. c ln3
ln4e2x
e4x 9dx .
5. c 0
12
(x2 + x 5) cos6x dx .
6. c 0
6
sin23x dx .
7. c cc 3
7dx
(x + 4) ln4(x + 4)
.
8. c , y = x2 + 7x + 3,
y = x 5 . .
9. c , c Ox ,
y =7
x + 3, x = 2 x = 0 .
10. ,
CM = 12q5 + 15q4 + 6q , 460 .
. 12 300 2012/2013 .
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MA , 3, 013
1. c (10x + 4) 5x2 + 4x 7 dx .
2. c 10(x2 + x + 4)
x3 2x2 + 10xdx .
3. c x
9 7 x34dx .
4. c 0
6
sin3x
cos23x 36dx
5. c 0
3
arctg x dx .
6. c 0
2
cos6x sin2x dx .
7. c cc
1dx
1 + x2
.
8. c , y = 4x2 + 4x + 7,
y = 5x2 + 6x + 10 . .
9. c , c Ox ,
y =2
x 6, x = 0 x = 5 .
10. ,
: z(t) = 1 . 264t2 + 8 . 7t + 6 . 2 t
( ), .
. 13 300 2012/2013 .
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MA , 3, 014
1. c (14x + 5) 7x2 + 5x + 217 dx .
2. c 20(x2 2x + 3)
(x + 1)(x2 6x + 13)dx .
3. c 2 x
5 + 9 x34dx .
4. c 12
716
2 tg34x + tg4x + 1
cos24xdx .
5. c 0
6
(x2 + 5x + 1) cos3x dx .
6. c 0
18
sin26x dx .
7. c cc 1
+
75x+4 dx
.
8. c , x + y = 6, yx = 5 .
.
9. c , c Ox ,
y =1
x + 3, x = 2 x = 2 .
10. ()
8 20
f (t) = 70000 + 75t 3t2, t , 8 t 20.
, 11 16 ,
1 4 . .
. 14 300 2012/2013 .
-
MA , 3, 015
1. c dx(4 + x)102 .
2. c 10(x2 2x 9)
(x + 7)(x + 3)(x 2)dx .
3. c dxx2
3 + 3 x.
4. c 0
10
sin5x
cos25x 36dx
5. c 1
3
1
arctg x dx .
6. c 0
18
sin26x dx .
7. c cc 1
265 + 2 x 1
x 1dx
.
8. c , y = 2x2 x 5,
y = 4x2 9x 5 . .
9. c , c Ox ,
y = x2 4x y = 0 x [6, 7] .
10.
e t (t )
V(t) = 78 + 8 cos
4(t + 6)
. .
. 15 300 2012/2013 .
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MA , 3, 016
1. c dx6 2x .
2. c x2 5x 2
(x 7)(x2 12x + 36)dx .
3. c x + 9 7
x + 13dx .
4. c e3
6
e11
6dx
x ln6x.
5. c 12
12 3
arctg2x dx .
6. c 0
24
sin26x dx .
7. c cc 52
+
62x1 dx
.
8. c , y = 5x2 + 4x + 5,
y = 2x2 3x + 5 . .
9. c , c Ox ,
y =5
x 6, x = 3 x = 0 .
10.
MC(x) = 6 2x 4x2, 67 .
.
. 16 300 2012/2013 .
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MA , 3, 017
1. c dx2x + 7 .
2. c 4(x2 5x 8)
x3 12x2 + 32xdx .
3. c 5 xx + 4 + 2 dx .
4. c 12
14
5 ctg3x + 2 ctg2x 3
sin2xdx .
5. c 0
8
(x2 x 2) cos4x dx .
6. c 0
24
cos26x dx .
7. c cc 2
dx
4 + x2
.
8. c , yx = 42, x + y = 13 .
.
9. c , c Ox ,
y =4
x + 2, x = 3 x = 6 .
10. K(t),
( , )
I(t) = 220 t74 , K(0) = 470 .
. 17 300 2012/2013 .
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MA , 3, 018
1. c dx(1 + x2) arctg8x .
2. c 2x2 + 8x + 14
2x2 x3dx .
3. c 4 x3
8 x23
dx .
4. c 13
38
3 tg36x + 2 tg6x 3
cos26xdx .
5. c 0
6
(x2 2x 4) cos3x dx .
6. c 0
10
sin25x dx .
7. c cc
10
sin5x dx
.
8. c , y = x2 6x 7,
y = 4x + 1 . .
9. c , c Ox ,
y =8
x 6, x = 6 x = 1 .
10. R(x), x
MR = 7x2 320 .
. 18 300 2012/2013 .
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MA , 3, 019
1. c dx(4 + 5x)30 .
2. c 8(x2 + 6x + 6)
(x + 2)(x2 + 4)dx .
3. c 1 xx 5 + 2 dx .
4. c ln2
ln4e3x
e6x + 4dx .
5. c 0
8
(x2 x + 2) cos4x dx .
6. c 0
2
sin5x sin3x dx .
7. c cc 12
45 4 4 x
4 xdx
.
8. c , y = 7x2 + 5x + 4,
y = 8x2 + x + 4 . .
9. c , c Ox ,
y = x2 3x y = 0 x [5, 6] .10. e
z(t) = 90t 8 . 94t2 , t ( ), .
C 8 . 64
, 29 .
. 19 300 2012/2013 .
-
MA , 3, 020
1. c arcsin x
1 x2dx .
2. c 2x2 + 8x 14
(x 1)(x2 + 2x + 1)dx .
3. c x + 4 6
x + 13dx .
4. c e44
e3
4dx
x ln34x.
5. c 14
3
14
arctg4x dx .
6. c 0
2
cos4x cos3x dx .
7. c cc 3
cos3x dx
.
8. c , y =1
x2 + 6, y =
1
7x2 .
.
9. c , c Ox ,
y =7
x + 1, x = 3 x = 9 .
10. R(x), x
MR = 9x5 230 .
. 20 300 2012/2013 .
-
MA , 3, 021
1. c dx5 6x .
2. c 5(x2 + 5x + 5)
(x + 2)(x2 + 2x + 5)dx .
3. c dxx2
3 + x.
4. c ln6
ln5e2x
4 9e4xdx .
5. c 0
12
(x2 + 3x 2) cos6x dx .
6. c 0
18
cos23x dx .
7. c cc
36
sin6x dx
.
8. c , yx = 42, x + y = 13 .
.
9. c , c Ox ,
y =1
x + 3, x = 0 x = 8 .
10. e
z(t) = 68t 7 . 46t2 , t ( ), .
C 8 . 11
, 55 .
. 21 300 2012/2013 .
-
MA , 3, 022
1. c dx4x 3 .
2. c 12(x2 7x + 2)
x3 4x2 12xdx .
3. c 5 4xx 1 + 1 dx .
4. c 54
12 tg3x + 2 tg2x + 1
cos2xdx .
5. c 1
2 3
12
arctg2x dx .
6. c 0
9
sin23x dx .
7. c cc 15e2
15
dx
x ln5x
.
8. c , x + y = 11, yx = 28 .
.
9. c , c Ox ,
y =4
x 4, x = 7 x = 3 .
10. q TC(q),
q
MC = e0.5q, 25 .
. 22 300 2012/2013 .
-
MA , 3, 023
1. c dx1 4x .
2. c 5(x2 3x 2)
(x + 1)(x2 + 4x + 8)dx .
3. c 3 xx 2 2 dx .
4. c 0
10
sin5x
cos25x 25dx
5. c 13
0
arctg3x dx .
6. c 0
15
sin25x dx .
7. c cc
0
e8xdx
.
8. c , y =36
x2 + 72,
y =1
108x2 . .
9. c , c Ox ,
y =6
x 4, x = 8 x = 1 .
10. R(x), x
MR = 5x9 380 .
. 23 300 2012/2013 .
-
MA , 3, 024
1. c dx2 6x .
2. c 2x2 + 14x 2
x3 + 4x2 + 4xdx .
3. c 7x + 2x 1 + 1 dx .
4. c e34
e5
4dx
x ln4x.
5. c 0
14
(x2 2x 3) cos7x dx .
6. c 0
2
cos3x sin4x dx .
7. c cc 12
1dx
1 x2
.
8. c , yx = 7, x + y = 8 .
.
9. c , c Ox ,
y =2
x 1, x = 6 x = 1 .
10. R(x), x
MR = 7x3 940 .
. 24 300 2012/2013 .
-
MA , 3, 025
1. c x 5x2 + 7 dx .
2. c 29(x2 3x + 5)
(x 7)(x2 4x + 8)dx .
3. c dxx2
3 2 x.
4. c ln3
ln4e2x
e4x 17dx .
5. c 13
13 3
arctg3x dx .
6. c 0
2
sin3x sin6x dx .
7. c cc 5
6x + 5
6 xdx
.
8. c , y = x2 + 4x, y = x2 .
.
9. c , c Ox ,
y = x2 + 6x y = 0 x [0, 2] .
10. ()
8 20
f (t) = 30000 + 63t 3t2, t , 8 t 20.
, 11 12 ,
1 2 . .
. 25 300 2012/2013 .
-
MA , 3, 026
1. c dx2 7x .
2. c 6(x2 6x + 3)
(x 2)(x 5)(x 4)dx .
3. c x
1 + x34
dx .
4. c 98
13 tg32x 5 tg2x 2
cos22xdx .
5. c 0
12
(x2 + 5x 5) sin6x dx .
6. c 0
2
cos6x sin2x dx .
7. c cc 34
+
84x+1 dx
.
8. c , y = 8x2 7x + 4,
y = 4x2 3x + 4 . .
9. c , c Ox ,
y = x2 + 3x y = 0 x [0, 1] .
10. K(t),
( , )
I(t) = 80(t 1)57 , ( t = 1)
310 .
. 26 300 2012/2013 .
-
MA , 3, 027
1. c dx(1 + 2x)83 .
2. c x2 7x 2
(x 2)(x2 11x + 30)dx .
3. c x 7 + 1
x 43dx .
4. c 128
128
2 tg37x 3 tg27x 1
cos27xdx .
5. c 0
13
3
arctg3x dx .
6. c 0
21
cos27x dx .
7. c cc 0
e8xdx
.
8. c , x + y = 8, yx = 7 .
.
9. c , c Ox ,
y = x2 + 4x y = 0 x [ 7, 6] .
10. K(t),
( , )
I(t) = 560(t 1)43 , K(1) = 890 .
. 27 300 2012/2013 .
-
MA , 3, 028
1. c dx(2x + 3)39 .
2. c 5(x2 3x + 7)
(x + 1)(x2 + 4)dx .
3. c 1 x 3
x 3 1dx .
4. c ln2
ln3e2x
e4x + 33dx .
5. c 12
12
3
arctg2x dx .
6. c 0
2
sin5x sin6x dx .
7. c cc
10
sin5x dx
.
8. c , y =4
x2 + 12, y =
1
16x2 .
.
9. c , c Ox ,
y =5
x 2, x = 5 x = 2 .
10. ()
8 20
f (t) = 4000 + 88t 3t2, t , 8 t 20.
, 14 19 ,
1 4 . .
. 28 300 2012/2013 .
-
MA , 3, 029
1. c dx(4 + 5x)82 .
2. c 4(x2 + 5x 6)
(x + 1)(x2 + 2x + 5)dx .
3. c x + 2x 2 + 1 dx .
4. c 14
38
3 ctg22x + 5 ctg2x + 2
sin22xdx .
5. c 13
3
13
arctg3x dx .
6. c 0
9
cos23x dx .
7. c cc
13
dx
1 + x2
.
8. c , x + y = 13, yx = 42 .
.
9. c , c Ox ,
y = x2 + 16 y = 0 x [0, 1] .
10. ,
: z(t) = 1 . 175t2 + 9 . 8t + 3 . 6 t
( ), .
. 29 300 2012/2013 .
-
MA , 3, 030
1. c x dx5x
2 325
2. c x2 + 6x + 6
(x + 1)(x2 + 3x + 2)dx .
3. c 7 + x 3
x 39dx .
4. c 512
13
2 tg23x + tg3x + 3
cos23xdx .
5. c 1
13
arctg x dx .
6. c 0
15
cos25x dx .
7. c cc 0
e5xdx
.
8. c , yx = 40, x + y = 13 .
.
9. c , c Ox ,
y =5
x + 4, x = 2 x = 8 .
10. ,
: z(t) = 1 . 271t2 + 8 . 5t + 0 . 1 t
( ), .
. 30 300 2012/2013 .
-
MA , 3, 031
1. c dx(4 + 3x)58 .
2. c 3x2 6x + 24
x3 3x2dx .
3. c 3 + x 2
x 18dx .
4. c 14
310
ctg35x + 3 ctg5x + 5
sin25xdx .
5. c 0
12
(x2 6x 6) cos6x dx .
6. c 0
42
sin27x dx .
7. c cc 3
7x + 2
x 3dx
.
8. c , y = x2 + 7x + 6,
y = 4x + 2 . .
9. c , c Ox ,
y =9
x + 9, x = 7 x = 1 .
10. e
z(t) = 68t 8 . 17t2 , t ( ), .
C 7 . 83
, 12 .
. 31 300 2012/2013 .
-
MA , 3, 032
1. c dx(1 + 4x)93 .
2. c 8(x2 3x 4)
x3 + 4x2 + 8xdx .
3. c 8 + xx 9 1 dx .
4. c 0
6
cos3x
sin23x 25dx
5. c 0
6
(x2 + x + 2) cos3x dx .
6. c 0
2
cos4x sin6x dx .
7. c cc
0
sin5x dx
.
8. c , x + y = 13, yx = 40 .
.
9. c , c Ox ,
y = x2 8x y = 0 x [ 1, 0] .
10.
MC(x) = 64 2x 8x2, 23 .
.
. 32 300 2012/2013 .
-
MA , 3, 033
1. c dx(2x 5)34 .
2. c 13(x2 3x + 5)
(x + 1)(x2 4x + 8)dx .
3. c 9 x + 2
x + 2 + 2dx .
4. c 136
112
ctg6x dx .
5. c 0
10
(x2 + 2x + 6) cos5x dx .
6. c 0
24
sin26x dx .
7. c cc 16
e7
6dx
x ln6x
.
8. c , y =25
x2 + 75,
y =1
100x2 . .
9. c , c Ox ,
y =7
x + 9, x = 8 x = 5 .
10. ,
: z(t) = 0 . 411t2 + 2 . 4t + 9 . 1 t
( ), .
. 33 300 2012/2013 .
-
MA , 3, 034
1. c (12x + 5) 6x2 + 5x 665 dx .
2. c x2 6x + 8
(x + 4)(x + 8)(x + 3)dx .
3. c 4 + xx 5 + 1 dx .
4. c ln3
ln4e2x
e4x 45dx .
5. c 0
6
(x2 x 6) sin3x dx .
6. c 0
30
cos25x dx .
7. c cc 1
12
dx
1 x2
.
8. c , y = x2 + 7x + 9,
y = 2x + 3 . .
9. c , c Ox ,
y = x2 1 y = 0 x [1, 3] .
10. ,
: z(t) = 0 . 625t2 + 6 . 6t + 1 . 2 t
( ), .
. 34 300 2012/2013 .
-
MA , 3, 035
1. c x dx 5x
2 + 695
2. c x2 + x 8
(x + 3)(x2 + 6x + 8)dx .
3. c dxx2
3 3 x.
4. c 542
17
tg7x dx .
5. c 0
12 3
arctg2x dx .
6. c 0
20
sin25x dx .
7. c cc 1
+
e3x1 dx
.
8. c , y = 3x2 8x + 2,
y = 5x2 6x + 6 . .
9. c , c Ox ,
y = x2 1 y = 0 x [ 4, 3] .
10.
e t (t )
V(t) = 67 + 2 sin
12(t + 9)
. .
. 35 300 2012/2013 .
-
MA , 3, 036
1. c 2x 2x2 2x 5
6dx .
2. c 2x2 14x + 4
(x 8)(x2 14x + 48)dx .
3. c dxx2
3 3 x.
4. c 524
724
3 ctg36x 4 ctg26x + 2
sin26xdx .
5. c 12 3
12
arctg2x dx .
6. c 0
28
sin27x dx .
7. c cc 1
dx
1 + x2
.
8. c , y = x2 + 2x + 3,
y = x 1 . .
9. c , c Ox ,
y = x2 6x y = 0 x [ 2, 1] .10. e
z(t) = 68t 8 . 41t2 , t ( ), .
C 8 . 15
, 70 .
. 36 300 2012/2013 .
-
MA , 3, 037
1. c (14x 3) 7x2 3x + 7 dx .
2. c 14(x2 2x 9)
(x + 5)(x 8)(x 2)dx .
3. c 8 + xx 8 1 dx .
4. c 0
12
cos6x
sin26x + 9dx
5. c 0
10
(x2 4x 6) sin5x dx .
6. c 0
2
cos6x cos3x dx .
7. c cc e24
e9
4dx
x2 + ln4x
.
8. c , y = 2x2 + 9x 1,
y = 5x2 + 6x 7 . .
9. c , c Ox ,
y = x2 5x y = 0 x [ 2, 0] .
10. R(x), x
MR = x2 620 .
. 37 300 2012/2013 .
-
MA , 3, 038
1. c dx2x + 6 .
2. c 18(x2 x + 8)
(x 2)(x2 4x 32)dx .
3. c 5x 1x 1 1 dx .
4. c 120
115
ctg5x dx .
5. c 0
4
(x2 7x 2) sin2x dx .
6. c 0
2
cos3x cos6x dx .
7. c cc e43
e5
3dx
x 5 + ln3x5
.
8. c , yx = 21, x + y = 10 .
.
9. c , c Ox ,
y =2
x + 1, x = 0 x = 3 .
10.
e t (t )
V(t) = 50 + 6 cos
2(t + 6)
. .
. 38 300 2012/2013 .
-
MA , 3, 039
1. c dx1 x2 arcsin6x
.
2. c 85(x2 + 4x + 7)
(x 7)(x2 + 4x + 8)dx .
3. c 2 xx + 3 + 1 dx .
4. c ln2
ln3e2x
e4x 7dx .
5. c 13
13 3
arctg3x dx .
6. c 0
2
sin7x sin4x dx .
7. c cc
72
e2x4 dx
.
8. c , y =16
x2 + 80, y =
1
96x2 .
.
9. c , c Ox ,
y = x2 2x y = 0 x [2, 5] .
10. ,
CM = 20q4 + 9q2 + 6q , 180 .
. 39 300 2012/2013 .
-
MA , 3, 040
1. c dx1 x2 arcsin x4
.
2. c 3x2 + 3x 21
x3 + 3x2dx .
3. c 7 x3
3 + 8 x23dx .
4. c ln2
ln3e2x
e4x 7dx .
5. c 12 3
12
arctg2x dx .
6. c 0
6
cos23x dx .
7. c cc 19
e5
9dx
x ln59x4
.
8. c , yx = 10, x + y = 7 .
.
9. c , c Ox ,
y = x2 2x y = 0 x [2, 3] .
10. ,
CM = 18q5 + 10q4 + 6q2, 400 .
. 40 300 2012/2013 .
-
MA , 3, 041
1. c dx(3 5x)93 .
2. c 10(x2 3x 2)
(x 3)(x2 8x + 25)dx .
3. c x + 4 4
x + 0dx .
4. c 0
6
cos3x
sin23x + 25dx
5. c 0
8
(x2 + 6x 3) sin4x dx .
6. c 0
10
sin25x dx .
7. c cc 52
+
72x2 dx
.
8. c , yx = 6, x + y = 5 .
.
9. c , c Ox ,
y =7
x + 8, x = 0 x = 4 .
10. e
z(t) = 83t 7 . 12t2 , t ( ), .
C 7 . 15
, 88 .
. 41 300 2012/2013 .
-
MA , 3, 042
1. c x dx4x
2 375
2. c 3x2 + 6x 15
x3 6x2 + 9xdx .
3. c 3x + 2x 3 + 1 dx .
4. c 0
6
sin3x
cos23x 36dx
5. c 1
13
arctg x dx .
6. c 0
2
cos5x sin3x dx .
7. c cc 1
dx
1 + x2
.
8. c , y =25
x2 + 100,
y =1
125x2 . .
9. c , c Ox ,
y =5
x 4, x = 5 x = 1 .
10. V(t) ,
, 0 . 38, . .
t V
V= 0 . 38t .
, 13 ,
, ,
V(0) = 25 .
. 42 300 2012/2013 .
-
MA , 3, 043
1. c 4x 32x2 3x + 6 dx .
2. c 18(x2 + 2x + 8)
(x + 3)(x2 + 9)dx .
3. c x + 5 + 2
5 + x + 5dx .
4. c e9
e4
9dx
x ln9x.
5. c 0
8
(x2 4x + 4) sin4x dx .
6. c 0
2
cos6x sin4x dx .
7. c cc 5
67 2 x 5
x 5dx
.
8. c , y = x2 + 4x + 15,
y = 3x + 3 . .
9. c , c Ox ,
y = x2 + 7x y = 0 x [0, 2] .
10. V(t) ,
, 0 . 19, . .
t V
V= 0 . 19t .
, 31 ,
, ,
V(0) = 11 .
. 43 300 2012/2013 .
-
MA , 3, 044
1. c (10x 3) 5x2 3x + 54 dx .
2. c 4(x2 + 2x 8)
(x + 3)(x2 + 6x + 13)dx .
3. c 3 x3
9 + 7 x23
dx .
4. c 0
142
tg7x dx .
5. c 0
14
(x2 + 6x + 3) cos7x dx .
6. c 0
2
cos5x cos3x dx .
7. c cc 61
32 3 x 1
3 xdx
.
8. c , y = 7x2,
y = 5x2 10x 6 . .
9. c , c Ox ,
y =1
x 2, x = 3 x = 5 .
10. V(t) ,
, 0 . 18, . .
t V
V= 0 . 18t .
31 , , V(0) = 28 .
. 44 300 2012/2013 .
-
MA , 3, 045
1. c dx(3x 2)41 .
2. c 5(x2 3x + 4)
x3 + 2x2 + 5xdx .
3. c 7 x + 6
x + 6 + 1dx .
4. c ln6
ln7e2x
e4x + 36dx .
5. c 0
6
(x2 + 7x + 3) sin3x dx .
6. c 0
12
sin24x dx .
7. c cc
1
e5x+4 dx
.
8. c , y =16
x2 + 112,
y =1
128x2 . .
9. c , c Ox ,
y = x2 + 3x y = 0 x [0, 3] .
10. ,
CM = 20q4 + 8q3 + 12q2, 380 .
. 45 300 2012/2013 .
-
MA , 3, 046
1. c x 4x2 77 dx .
2. c x2 6x + 8
x3 + x2 2xdx .
3. c 4 x + 4
x + 4 3dx .
4. c 16
14
tg4x dx .
5. c 0
4
(x2 + 3x 2) cos2x dx .
6. c 0
12
sin23x dx .
7. c cc 18
sin3x dx
.
8. c , y = 7x2,
y = 5x2 4x + 11 . .
9. c , c Ox ,
y = x2 + 6x y = 0 x [ 8, 6] .
10. e
z(t) = 64t 5 . 78t2 , t ( ), .
C 7 . 71
, 64 .
. 46 300 2012/2013 .
-
MA , 3, 047
1. c 10x + 45x2 + 4x 5
dx .
2. c 5(x2 8x + 4)
(x + 1)(x2 + 4)dx .
3. c 8 x
1 + 5 x34
dx .
4. c 16
14
tg4x dx .
5. c 0
10
(x2 + 5x + 4) cos5x dx .
6. c 0
9
sin23x dx .
7. c cc 5
545 x 5 6
x 5dx
.
8. c , y =1
x2 + 5, y =
1
6x2 .
.
9. c , c Ox ,
y =7
x 9, x = 8 x = 1 .
10. ()
8 20
f (t) = 8000 + 96t 3t2, t , 8 t 20.
, 15 17 ,
1 8 . .
. 47 300 2012/2013 .
-
MA , 3, 048
1. c dx(1 + x2) arctg6x7
.
2. c x2 8x + 6
x3 3x2 + 2xdx .
3. c 2 xx + 3 + 1 dx .
4. c ln3
ln4e2x
e4x 25dx .
5. c 13
13 3
arctg3x dx .
6. c 0
2
cos4x sin3x dx .
7. c cc 7
8x + 5
8 xdx
.
8. c , x + y = 12, yx = 35 .
.
9. c , c Ox ,
y = x2 4x y = 0 x [ 1, 0] .
10.
e t (t )
V(t) = 61 + 2 cos
12(t + 6)
. .
. 48 300 2012/2013 .
-
MA , 3, 049
1. c dx(5x 4)104 .
2. c 2x2 18x + 16
2x2 x3dx .
3. c 3 + x 2
x 18dx .
4. c 29
13
tg3x dx .
5. c 13
13 3
arctg3x dx .
6. c 0
2
cos3x sin4x dx .
7. c cc 1
dx
1 + x2
.
8. c , y =36
x2 + 180,
y =1
216x2 . .
9. c , c Ox ,
y = x2 9x y = 0 x [ 1, 0] .
10. V(t) ,
, 42% , . .
t V
V= 0 . 42t .
14 , , V(0) = 94 .
. 49 300 2012/2013 .
-
MA , 3, 050
1. c x 2x2 543 dx .
2. c x2 8x + 8
(x 5)(x2 12x + 36)dx .
3. c 5x 6x 1 + 1 dx .
4. c e72
e11
2dx
x ln2x.
5. c 12 3
12
arctg2x dx .
6. c 0
8
sin24x dx .
7. c cc
14
74x+3 dx
.
8. c , y = 9x2 + 5x 7,
y = 5x2 7x + 1 . .
9. c , c Ox ,
y =1
x + 7, x = 0 x = 3 .
10. R(x), x
MR = 3x4 670 .
. 50 300 2012/2013 .
-
MA , 3, 051
1. c dx2 6x .
2. c 25(x2 + 3x + 8)
(x 3)(x2 + 2x + 10)dx .
3. c 3x + 4x 3 1 dx .
4. c 0
12
sin6x
cos26x + 36dx
5. c 0
12 3
arctg2x dx .
6. c 0
21
cos27x dx .
7. c cc 0
e8xdx
.
8. c , y = x2 + 11x + 7,
y = 4x 3 . .
9. c , c Ox ,
y =3
x + 2, x = 6 x = 4 .
10. ,
CM = 8q3 + 12q2 + 8q , 570 .
. 51 300 2012/2013 .
-
MA , 3, 052
1. c dx8x + 3 .
2. c 13(x2 + 4x 3)
(x 2)(x2 + 2x + 5)dx .
3. c 2 + x 3
x 28dx .
4. c 916
12
3 tg34x 4 tg24x + 3
cos24xdx .
5. c 12
12
3
arctg2x dx .
6. c 0
15
cos25x dx .
7. c cc e64
e4
4dx
x6 + ln4x
.
8. c , y =4
x2 + 20, y =
1
24x2 .
.
9. c , c Ox ,
y =6
x 2, x = 6 x = 1 .
10. ,
: z(t) = 0 . 932t2 + 9 . 3t + 1 . 1 t
( ), .
. 52 300 2012/2013 .
-
MA , 3, 053
1. c 4x + 72x2 + 7x + 2
dx .
2. c 8(x2 + 2x + 3)
x3 + 4x2 + 8xdx .
3. c x + 3 + 3
x + 39dx .
4. c ln3
ln4e2x
e4x 65dx .
5. c 0
6
(x2 5x + 1) sin3x dx .
6. c 0
2
cos6x sin3x dx .
7. c cc
23
e3x3 dx
.
8. c , x + y = 8, yx = 15 .
.
9. c , c Ox ,
y =3
x 3, x = 8 x = 2 .
10.
e t (t )
V(t) = 87 + 2 cos
4(t + 6)
. .
. 53 300 2012/2013 .
-
MA , 3, 054
1. c dx(3 + x)98 .
2. c 85(x2 2x + 1)
(x + 8)(x2 2x + 5)dx .
3. c x 1 8
1 + x 1dx .
4. c ln6
ln5e2x
4 81e4xdx .
5. c 12 3
12
arctg2x dx .
6. c 0
4
cos22x dx .
7. c cc 4
5x + 4
5 xdx
.
8. c , yx = 15, x + y = 8 .
.
9. c , c Ox ,
y = x2 + 2x y = 0 x [0, 3] .10.
e t (t )
V(t) = 12 + 6 sin
12(t + 2)
. .
. 54 300 2012/2013 .
-
MA , 3, 055
1. c x dx4x
2 387
2. c 3x2 3x + 12
x3 3x2dx .
3. c 8x 5x 1 + 1 dx .
4. c 58
12
5 tg32x + 5 tg22x + 2
cos22xdx .
5. c 3
0
arctg x dx .
6. c 0
4
cos22x dx .
7. c cc 15e7
15
dx
x ln5x
.
8. c , y =9
x2 + 36, y =
1
45x2 .
.
9. c , c Ox ,
y = x2 3x y = 0 x [5, 6] .10.
MC(x) = 74 4x 3x2, 38 .
.
. 55 300 2012/2013 .
-
MA , 3, 056
1. c dx4 8x .
2. c 13(x2 + 4x 5)
(x + 6)(x2 + 6x + 13)dx .
3. c x 1 + 4
x + 15dx .
4. c ln3
ln6e2x
e4x 16dx .
5. c 13
13 3
arctg3x dx .
6. c 0
18
cos26x dx .
7. c cc
e2xdx
.
8. c , x + y = 13, yx = 36 .
.
9. c , c Ox ,
y = x2 + 6x y = 0 x [1, 2] .
10. e
z(t) = 58t 7 . 61t2 , t ( ), .
C 7 . 69
, 49 .
. 56 300 2012/2013 .
-
MA , 3, 057
1. c 14x 57x
2 5x + 217
dx .
2. c 3(x2 + 3x 4)
x3 + 4x2 + 3xdx .
3. c 1 + xx 1 1 dx .
4. c 0
12
sin6x
cos26x 9dx
5. c 0
13
3
arctg3x dx .
6. c 0
30
cos25x dx .
7. c cc
0
e7xdx
.
8. c , yx = 21, x + y = 10 .
.
9. c , c Ox ,
y = x2 8x y = 0 x [ 2, 0] .
10. V(t) ,
, 0 . 34, . .
t V
V= 0 . 34t .
, 13 ,
, ,
V(0) = 81 .
. 57 300 2012/2013 .
-
MA , 3, 058
1. c (2x + 1)51dx .
2. c 13(x2 + 5x + 7)
x3 + 6x2 + 13xdx .
3. c 3 + 4xx 2 + 1 dx .
4. c 0
6
cos3x
sin23x + 25dx
5. c 0
12
(x2 + 3x 3) cos6x dx .
6. c 0
20
sin25x dx .
7. c cc 53
6
8dx
(x + 9) ln9(x + 9)
.
8. c , y = x2 + 1,
y = 4x + 4 . .
9. c , c Ox ,
y = x2 4 y = 0 x [ 4, 2] .10. V(t) ,
, 35% , . .
t V
V= 0 . 35t .
, 13 ,
, ,
V(0) = 56 .
. 58 300 2012/2013 .
-
MA , 3, 059
1. c x dx 5x
2 + 645
2. c 18(x2 6x 4)
x3 36xdx .
3. c x 2x 3 1 dx .
4. c 19
118
ctg3x dx .
5. c 0
14
(x2 + 6x + 4) cos7x dx .
6. c 0
8
sin22x dx .
7. c cc 8
176 5 x 8
x 8dx
.
8. c , y = 4x2 x,
y = 7x2 + 5x + 9 . .
9. c , c Ox ,
y = x2 9 y = 0 x [3, 4] .
10. e
z(t) = 56t 6 . 07t2 , t ( ), .
C 7 . 77
, 89 .
. 59 300 2012/2013 .
-
MA , 3, 060
1. c (1 3x)93dx .
2. c 8(x2 8x 3)
(x + 2)(x2 + 4)dx .
3. c 8 + x + 7
x + 7 + 1dx .
4. c ln2
ln4e3x
e6x + 4dx .
5. c 12 3
12
arctg2x dx .
6. c 0
2
cos3x sin6x dx .
7. c cc e74
e2
4dx
x (7 + ln4x)94
.
8. c , x + y = 8, yx = 7 .
.
9. c , c Ox ,
y = x2 + x y = 0 x [ 4, 1] .10.
e t (t )
V(t) = 97 + 8 cos
3(t + 5)
. .
. 60 300 2012/2013 .
-
MA , 3, 061
1. c x dx5x2 3
.
2. c 8(x2 + 2x + 4)
x3 4x2 + 8xdx .
3. c dxx2
3 + 5 x.
4. c ln4
ln7e2x
e4x + 16dx .
5. c 0
6
(x2 x 7) cos3x dx .
6. c 0
2
cos5x cos4x dx .
7. c cc 4
534 x 4 + 5
x 4dx
.
8. c , y = 7x2 + 3x + 3,
y = 5x2 11x + 3 . .
9. c , c Ox ,
y = x2 + 8x y = 0 x [1, 2] .
10. e
z(t) = 84t 8 . 56t2 , t ( ), .
C 8 . 26
, 87 .
. 61 300 2012/2013 .
-
MA , 3, 062
1. c dx(4 5x)84 .
2. c x2 4x 5
x3 2x2 + xdx .
3. c x 4x 5 2 dx .
4. c 0
14
cos7x
sin27x + 9dx
5. c 0
8
(x2 5x 2) sin4x dx .
6. c 0
2
cos4x sin6x dx .
7. c cc 4
5x 7
x + 4dx
.
8. c , y =4
x2 + 24, y =
1
28x2 .
.
9. c , c Ox ,
y =8
x 1, x = 6 x = 0 .
10. e
z(t) = 55t 6 . 15t2 , t ( ), .
C 8 . 47
, 51 .
. 62 300 2012/2013 .
-
MA , 3, 063
1. c (14x + 6) 7x2 + 6x + 58 dx .
2. c 73(x2 x + 4)
(x + 8)(x2 + 9)dx .
3. c dxx2
3 3 x.
4. c 0
12
cos6x
sin26x 25dx
5. c 0
12
(x2 6x + 6) sin6x dx .
6. c 0
2
cos6x sin3x dx .
7. c cc 1
+
ex5 dx
.
8. c , y = 7x2 5x 6,
y = 10x2 14x + 6 . .
9. c , c Ox ,
y = x2 5x y = 0 x [5, 6] .
10. V(t) ,
, 39% , . .
t V
V= 0 . 39t .
, 13 ,
, ,
V(0) = 24 .
. 63 300 2012/2013 .
-
MA , 3, 064
1. c x 2x2 3 dx .
2. c x2 + 7x + 6
(x 2)(x2 9x + 18)dx .
3. c 5x + 2x 1 + 1 dx .
4. c 0
8
cos4x
sin24x + 36dx
5. c 14
14 3
arctg4x dx .
6. c 0
30
cos25x dx .
7. c cc
4
sin4x dx
.
8. c , x + y = 11, yx = 28 .
.
9. c , c Ox ,
y = x2 + 4x y = 0 x [0, 2] .
10. R(x), x
MR = 3x4 660 .
. 64 300 2012/2013 .
-
MA , 3, 065
1. c arctg6x7
1 + x2dx .
2. c 5(x2 + 2x 9)
x3 8x2 + 15xdx .
3. c 8 + x 4
x + 32dx .
4. c ln2
ln7e2x
e4x + 4dx .
5. c 12
12 3
arctg2x dx .
6. c 0
2
cos5x sin3x dx .
7. c cc 5
3
dx
25 + x2
.
8. c , y =16
x2 + 64, y =
1
80x2 .
.
9. c , c Ox ,
y = x2 8x y = 0 x [ 3, 0] .10. e
z(t) = 59t 7 . 14t2 , t ( ), .
C 8 . 48
, 71 .
. 65 300 2012/2013 .
-
MA , 3, 066
1. c arctg4x3
1 + x2dx .
2. c 85(x2 + x + 5)
(x + 9)(x2 + 4)dx .
3. c x 7 9
x + 2dx .
4. c 58
34
4 ctg22x ctg2x + 4
sin22xdx .
5. c 0
4
(x2 2x + 5) cos2x dx .
6. c 0
2
cos3x sin2x dx .
7. c cc 1
0dx
1 x2
.
8. c , y =36
x2 + 216,
y =1
252x2 . .
9. c , c Ox ,
y = x2 6x y = 0 x [ 2, 1] .10.
e t (t )
V(t) = 83 + 4 cos
3(t + 4)
. .
. 66 300 2012/2013 .
-
MA , 3, 067
1. c dx8 5x .
2. c x2 + 7x + 4
(x + 4)(x + 5)(x + 3)dx .
3. c 3 + x 3
x 28dx .
4. c e5
e6
5dx
x ln25x.
5. c 0
8
(x2 4x + 4) sin4x dx .
6. c 0
2
cos3x cos5x dx .
7. c cc 2
5dx
(x 1) ln(x 1)
.
8. c , y = 4x2 + x + 1,
y = 6x2 11x 9 . .
9. c , c Ox ,
y = x2 1 y = 0 x [ 4, 2] .
10. q TC(q),
q
MC = e5.9q, 26 .
. 67 300 2012/2013 .
-
MA , 3, 068
1. c x 7x2 56 dx .
2. c 2x2 6x + 16
2x2 x3dx .
3. c dxx x3
.
4. c ln6
ln7e2x
e4x 49dx .
5. c 14
14 3
arctg4x dx .
6. c 0
2
cos6x sin4x dx .
7. c cc
1dx
1 + x2
.
8. c , y = 8x2 5x 7,
y = 2x2 + 7x 7 . .
9. c , c Ox ,
y = x2 7x y = 0 x [8, 9] .
10. ,
CM = 16q3 + 6q2 + 6q , 740 .
. 68 300 2012/2013 .
-
MA , 3, 069
1. c dx(5x + 3)39 .
2. c 5(x2 3x + 6)
x3 2x2 + 5xdx .
3. c x 2 7
x 27dx .
4. c 0
6
cos3x
sin23x + 36dx
5. c 0
14 3
arctg4x dx .
6. c 0
24
sin24x dx .
7. c cc 0
1dx
1 x2
.
8. c , y = 7x2 3x 8,
y = 6x2 + 3x 1 . .
9. c , c Ox ,
y = x2 6x y = 0 x [ 6, 0] .
10. e
z(t) = 78t 7 . 22t2 , t ( ), .
C 8 . 20
, 63 .
. 69 300 2012/2013 .
-
MA , 3, 070
1. c (4x + 3)57dx .
2. c 5(x2 7x + 1)
(x 1)(x2 4x + 8)dx .
3. c x + 6 7
x 3dx .
4. c ln5
ln4e2x
4 25e4xdx .
5. c 0
6
(x2 + 6x 2) cos3x dx .
6. c 0
2
sin3x sin5x dx .
7. c cc
2
cos x dx
.
8. c , y =49
x2 + 294,
y =1
343x2 . .
9. c , c Ox ,
y = x2 + 7x y = 0 x [0, 2] .
10. e
z(t) = 59t 5 . 47t2 , t ( ), .
C 8 . 18
, 31 .
. 70 300 2012/2013 .
-
MA , 3, 071
1. c dx1 x2 arcsin4x
3.
2. c 5(x2 + 6x 4)
x3 2x2 + 5xdx .
3. c x 4 + 6
x + 12dx .
4. c e6
e5
6dx
x ln6x.
5. c 13
3
0
arctg3x dx .
6. c 0
2
cos5x sin6x dx .
7. c cc
48
cos8x dx
.
8. c , y = x2 + 2x + 7,
y = 4x 1 . .
9. c , c Ox ,
y = x2 1 y = 0 x [ 3, 1] .10. V(t) ,
, 16% , . .
t V
V= 0 . 16t .
, 31 ,
, ,
V(0) = 47 .
. 71 300 2012/2013 .
-
MA , 3, 072
1. c (12x + 7) 6x2 + 7x + 56 dx .
2. c 4(x2 x + 7)
(x 2)(x2 4x + 8)dx .
3. c 2 x
1 9 x34dx .
4. c ln5
ln6e2x
e4x 16dx .
5. c 0
4
(x2 4x + 6) sin2x dx .
6. c 0
36
cos26x dx .
7. c cc
43
dx
16 + x2
.
8. c , y = x2 2x 3,
y = 4x + 5 . .
9. c , c Ox ,
y = x2 + 7x y = 0 x [1, 2] .10.
MC(x) = 26 4x 2x2, 76 .
.
. 72 300 2012/2013 .
-
MA , 3, 073
1. c (10x 1) 5x2 x 6 dx .
2. c 10(x2 + 3x + 7)
x3 + 2x2 + 10xdx .
3. c x + 7x 7 + 1 dx .
4. c e28
e1
8dx
x ln38x.
5. c 0
8
(x2 + 7x 4) cos4x dx .
6. c 0
12
cos24x dx .
7. c cc
30
sin5x dx
.
8. c , y = 7x2 + 8x 6,
y = 6x2 + 6x 6 . .
9. c , c Ox ,
y = x2 + 8x y = 0 x [0, 1] .
10. ,
: z(t) = 1 . 123t2 + 6 . 1t + 5 . 6 t
( ), .
. 73 300 2012/2013 .
-
MA , 3, 074
1. c (6x 2) 3x2 2x + 5 dx .
2. c x2 5x 7
(x 3)(x2 8x + 16)dx .
3. c 8 x3
3 x23
dx .
4. c 320
15
tg5x dx .
5. c 0
10
(x2 + x 6) sin5x dx .
6. c 0
2
cos5x sin3x dx .
7. c cc
4
sin4x dx
.
8. c , yx = 21, x + y = 10 .
.
9. c , c Ox ,
y =5
x 9, x = 1 x = 7 .
10. ()
8 20
f (t) = 5000 + 86t 3t2, t , 8 t 20.
, 15 19 ,
1 9 . .
. 74 300 2012/2013 .
-
MA , 3, 075
1. c dx5x 4 .
2. c 13(x2 2x 7)
(x + 3)(x2 + 4)dx .
3. c 8 + x 1
x + 3dx .
4. c 0
10
sin5x
cos25x 16dx
5. c 0
14
(x2 2x + 4) cos7x dx .
6. c 0
15
sin25x dx .
7. c cc 14
e6
4dx
x ln84x
.
8. c , y =36
x2 + 144,
y =1
180x2 . .
9. c , c Ox ,
y = x2 3x y = 0 x [ 3, 0] .
10. R(x), x
MR = 4x5 630 .
. 75 300 2012/2013 .
-
MA , 3, 076
1. c (12x + 7) 6x2 + 7x 4 dx .
2. c 9(x2 3x + 3)
(x 2)(x2 4x + 13)dx .
3. c 3x + 1x 3 + 1 dx .
4. c 54
32
4 ctg3x + ctg x + 3
sin2xdx .
5. c 0
12
(x2 + 5x + 1) cos6x dx .
6. c 0
2
sin5x sin4x dx .
7. c cc 6
15x 6 + 5
x 6dx
.
8. c , y = 4x2 7x + 2,
y = 3x2 2x 4 . .
9. c , c Ox ,
y =2
x + 8, x = 6 x = 4 .
10. ()
8 20
f (t) = 3000 + 96t 3t2, t , 8 t 20.
, 11 14 ,
1 6 . .
. 76 300 2012/2013 .
-
MA , 3, 077
1. c dx(5 + 4x)88 .
2. c x2 + 7x 1
(x + 5)(x2 + 11x + 30)dx .
3. c x 1x 3 + 2 dx .
4. c 14
13
2 tg23x + 5 tg3x + 3
cos23xdx .
5. c 12 3
12
arctg2x dx .
6. c 0
10
sin25x dx .
7. c cc e53
e2
3dx
x5 + ln3x8
.
8. c , y = 6x2 + 2x + 1,
y = 7x2 3x 5 . .
9. c , c Ox ,
y =4
x + 7, x = 2 x = 4 .
10. ,
CM = 24q5 + 15q4 + 8q , 410 .
. 77 300 2012/2013 .
-
MA , 3, 078
1. c arcsin x1 x2
dx .
2. c 5(x2 + 4x 8)
(x + 5)(x2 + 12x + 40)dx .
3. c 1 6xx 2 + 1 dx .
4. c 0
12
cos6x
sin26x 4dx
5. c 1
0
arctg x dx .
6. c 0
2
cos6x cos2x dx .
7. c cc 6
3dx
(x + 7) ln(x + 7)
.
8. c , x + y = 16, yx = 63 .
.
9. c , c Ox ,
y = x2 + 6x y = 0 x [0, 1] .
10. q TC(q),
q
MC = e4.7q, 95 .
. 78 300 2012/2013 .
-
MA , 3, 079
1. c dx(3x 1)97 .
2. c 13(x2 3x 2)
(x 5)(x2 4x + 8)dx .
3. c x + 3 + 1
3 x + 3dx .
4. c 17
328
4 tg37x + 4 tg27x 1
cos27xdx .
5. c 0
13
3
arctg3x dx .
6. c 0
2
cos3x sin4x dx .
7. c cc
e8xdx
.
8. c , x + y = 7, yx = 10 .
.
9. c , c Ox ,
y =1
x + 8, x = 2 x = 9 .
10. R(x), x
MR = 7x6 750 .
. 79 300 2012/2013 .
-
MA , 3, 080
1. c dx5 2x .
2. c 3x2 9x 15
(x 1)(x2 5x + 4)dx .
3. c x3
7 x23
dx .
4. c e2
e2
2dx
x ln72x.
5. c 0
8
(x2 + 3x 4) sin4x dx .
6. c 0
36
cos26x dx .
7. c cc 1
3x + 1
3 xdx
.
8. c , y = x2 6x 6,
y = x2 + 2x + 4 . .
9. c , c Ox ,
y = x2 + 4x y = 0 x [0, 1] .10. q TC(q),
q
MC = e1.2q, 48 .
. 80 300 2012/2013 .
-
MA , 3, 081
1. c (8x 1) 4x2 x + 47 dx .
2. c 17(x2 x + 3)
x3 + 2x2 + 17xdx .
3. c x + 7 7
x + 32dx .
4. c ln4
ln7e2x
e4x 25dx .
5. c 12
0
arctg2x dx .
6. c 0
2
cos4x sin3x dx .
7. c cc 12
sin2x dx
.
8. c , y = x2 + 5x 23,
y = 4x 3 . .
9. c , c Ox ,
y =5
x 5, x = 8 x = 0 .
10. V(t) ,
, 34% , . .
t V
V= 0 . 34t .
, 13 ,
, ,
V(0) = 25 .
. 81 300 2012/2013 .
-
MA , 3, 082
1. c dx3x 5 .
2. c 9(x2 + 4x + 6)
(x + 1)(x2 + 2x + 10)dx .
3. c 6 + x 1
x 1 + 1dx .
4. c ln5
ln4e2x
9 16e4xdx .
5. c 12
0
arctg2x dx .
6. c 0
24
sin26x dx .
7. c cc 7
2x 5 + 6 2 x
2 xdx
.
8. c , y = x2 + 3x + 8,
y = 2x2 + 5x + 8 . .
9. c , c Ox ,
y = x2 36 y = 0 x [6, 7] .10.
MC(x) = 82 x x2, 13 .
.
. 82 300 2012/2013 .
-
MA , 3, 083
1. c (3 + 4x)84dx .
2. c 10(x2 + 3x + 6)
(x + 3)(x2 + 4x + 13)dx .
3. c x 4x + 2 1 dx .
4. c ln2
ln3e2x
e4x + 20dx .
5. c 0
8
(x2 5x 4) sin4x dx .
6. c 0
2
cos6x sin7x dx .
7. c cc
25
85x+1 dx
.
8. c , yx = 63, x + y = 16 .
.
9. c , c Ox ,
y = x2 + 4x y = 0 x [0, 2] .
10. ,
CM = 10q4 + 12q3 + 9q2, 970 .
. 83 300 2012/2013 .
-
MA , 3, 084
1. c dx6 7x .
2. c 20(x2 3x + 6)
(x 4)(x2 4x + 20)dx .
3. c x 1x + 2 + 2 dx .
4. c 0
6
cos3x
sin23x + 16dx
5. c 13 3
13
arctg3x dx .
6. c 0
2
cos3x sin5x dx .
7. c cc
6
ex dx
.
8. c , yx = 14, x + y = 9 .
.
9. c , c Ox ,
y = x2 9 y = 0 x [ 5, 4] .
10. R(x), x
MR = 5x 700 .
. 84 300 2012/2013 .
-
MA , 3, 085
1. c arctg x3
1 + x2dx .
2. c 8(x2 5x 5)
(x 5)(x2 14x + 53)dx .
3. c 7 + 2xx 4 + 1 dx .
4. c ln4
ln7e2x
e4x 36dx .
5. c 12
12 3
arctg2x dx .
6. c 0
15
sin25x dx .
7. c cc 0
dx
81 + x2
.
8. c , yx = 12, x + y = 7 .
.
9. c , c Ox ,
y = x2 1 y = 0 x [ 3, 2] .
10. q TC(q),
q
MC = e8.4q, 47 .
. 85 300 2012/2013 .
-
MA , 3, 086
1. c dx4 7x .
2. c 5(x2 + 4x 4)
(x + 4)(x2 + 10x + 29)dx .
3. c x + 8 8
x + 33dx .
4. c 128
121
tg7x dx .
5. c 1
2 3
12
arctg2x dx .
6. c 0
2
cos7x sin4x dx .
7. c cc 12
1dx
1 x2
.
8. c , y = 5x2 + 2x + 6,
y = 3x2 6x 4 . .
9. c , c Ox ,
y = x2 + 4x y = 0 x [0, 1] .10. e
z(t) = 84t 7 . 67t2 , t ( ), .
C 7 . 86
, 38 .
. 86 300 2012/2013 .
-
MA , 3, 087
1. c dx(2x 3)78 .
2. c 10(x2 5x + 1)
x3 2x2 + 10xdx .
3. c 6 + x 6
x + 30dx .
4. c e38
e2
8dx
x ln28x.
5. c 13
13 3
arctg3x dx .
6. c 0
2
cos6x sin5x dx .
7. c cc 2
3dx
(x 1) ln(x 1)
.
8. c , y =4
x2 + 8, y =
1
12x2 .
.
9. c , c Ox ,
y =1
x + 7, x = 0 x = 1 .
10. e
z(t) = 55t 7 . 55t2 , t ( ), .
C 7 . 76
, 61 .
. 87 300 2012/2013 .
-
MA , 3, 088
1. c dx4 2x .
2. c 2x2 6x + 4
2x2 x3dx .
3. c dxx 3 x3
.
4. c ln5
ln6e2x
e4x 36dx .
5. c 0
8
(x2 + x 1) cos4x dx .
6. c 0
15
cos25x dx .
7. c cc
0
cos5x dx
.
8. c , y = x2 x + 15,
y = 2x + 5 . .
9. c , c Ox ,
y =5
x 5, x = 6 x = 1 .
10. ,
: z(t) = 1 . 067t2 + 5 . 5t + 6 . 3 t
( ), .
. 88 300 2012/2013 .
-
MA , 3, 089
1. c (8x 7) 4x2 7x + 578 dx .
2. c x2 + 7x + 5
(x + 5)(x2 + 8x + 16)dx .
3. c 8 3xx + 3 + 1 dx .
4. c 0
8
cos4x
sin24x + 9dx
5. c 12
12 3
arctg2x dx .
6. c 0
2
cos5x cos6x dx .
7. c cc
43
e3x+3 dx
.
8. c , y = 2x2 6x + 1,
y = x2 3x + 1 . .
9. c , c Ox ,
y = x2 16 y = 0 x [ 6, 5] .
10. V(t) ,
, 0 . 26, . .
t V
V= 0 . 26t .
12 , , V(0) = 41 .
. 89 300 2012/2013 .
-
MA , 3, 090
1. c (14x + 6) 7x2 + 6x 718 dx .
2. c x2 x + 6
x2 x3dx .
3. c 7 x + 8
x + 8 + 2dx .
4. c 0
6
cos3x
sin23x 25dx
5. c 0
12
(x2 4x 5) cos6x dx .
6. c 0
18
sin23x dx .
7. c cc 2
6x 5
6 xdx
.
8. c , y = x2 + 3x 3,
y = 2x + 3 . .
9. c , c Ox ,
y = x2 4 y = 0 x [ 4, 3] .
10. R(x), x
MR = x6 770 .
. 90 300 2012/2013 .
-
MA , 3, 091
1. c dx3x 2 .
2. c 3x2 + 9x + 24
(x + 4)(x2 + 5x + 4)dx .
3. c 5 xx + 2 2 dx .
4. c ln3
ln6e2x
e4x 36dx .
5. c 0
14
(x2 3x + 2) cos7x dx .
6. c 0
4
cos22x dx .
7. c cc e76
e6
6dx
x (7 + ln6x)5
.
8. c , y = 8x2 + 4x,
y = 7x2 + 5x . .
9. c , c Ox ,
y =9
x + 8, x = 6 x = 9 .
10. V(t) ,
, 27% , . .
t V
V= 0 . 27t .
, 22 a,
, ,
V(0) = 18 .
. 91 300 2012/2013 .
-
MA , 3, 092
1. c dx1 6x .
2. c x2 + 5x 5
(x + 3)(x2 + 4x + 4)dx .
3. c 3x 7x + 4 + 1 dx .
4. c 0
6
sin3x
cos23x 9dx
5. c 13
13 3
arctg3x dx .
6. c 0
6
sin22x dx .
7. c cc
sin7x dx
.
8. c , y =49
x2 + 196,
y =1
245x2 . .
9. c , c Ox ,
y = x2 + 5x y = 0 x [0, 4] .10. R(x), x
MR = 7x4 410 .
. 92 300 2012/2013 .
-
MA , 3, 093
1. c dx1 x2 arcsin x6
.
2. c 20(x2 + 3x + 1)
(x 4)(x2 + 4)dx .
3. c x + 7 + 2
x + 16dx .
4. c 0
6
sin3x
cos23x 16dx
5. c 1
13
arctg x dx .
6. c 0
9
sin23x dx .
7. c cc 15
+
35x3 dx
.
8. c , yx = 20, x + y = 9 .
.
9. c , c Ox ,
y = x2 3x y = 0 x [4, 5] .
10. K(t),
( , )
I(t) = 880 t74 , K(0) = 650 .
. 93 300 2012/2013 .
-
MA , 3, 094
1. c (5 2x)33dx .
2. c 2x2 + 14x + 10
2x2 x3dx .
3. c 2 + x + 6
x + 31dx .
4. c 0
6
sin3x
cos23x + 16dx
5. c 0
1
arctg x dx .
6. c 0
24
cos24x dx .
7. c cc 13
+
33x+2 dx
.
8. c , y =16
x2 + 80, y =
1
96x2 .
.
9. c , c Ox ,
y =5
x 6, x = 7 x = 5 .
10. ,
CM = 24q5 + 8q3 + 9q2, 430 .
. 94 300 2012/2013 .
-
MA , 3, 095
1. c (5x + 2)92dx .
2. c 4(x2 3x + 8)
x3 12x2 + 32xdx .
3. c 2 + xx 1 + 1 dx .
4. c 0
14
cos7x
sin27x + 25dx
5. c 0
10
(x2 4x 6) cos5x dx .
6. c 0
21
cos27x dx .
7. c cc 12
cos2x dx
.
8. c , x + y = 3, yx = 2 .
.
9. c , c Ox ,
y = x2 4x y = 0 x [ 1, 0] .10. V(t) ,
, 0 . 24, . .
t V
V= 0 . 24t .
12 , , V(0) = 26 .
. 95 300 2012/2013 .
-
MA , 3, 096
1. c (4x 5) 2x2 5x 487 dx .
2. c x2 x + 6
(x 3)(x 6)(x 5)dx .
3. c x + 8 4
x + 17dx .
4. c 116
03 tg24x + 4 tg4x 1
cos24xdx .
5. c 0
6
(x2 + 7x + 1) cos3x dx .
6. c 0
18
sin26x dx .
7. c cc 0
3dx
(x + 1) ln(x + 1)
.
8. c , y = x2 + x 8,
y = 5x 3 . .
9. c , c Ox ,
y = x2 5x y = 0 x [ 2, 1] .10.
MC(x) = 21 8x 3x2, 64 .
.
. 96 300 2012/2013 .
-
MA , 3, 097
1. c dx(3 + 5x)70 .
2. c x2 + 5x + 8
(x + 6)(x2 + 10x + 25)dx .
3. c 8 xx + 9 + 1 dx .
4. c 18
0tg32x 2 tg22x + 4
cos22xdx .
5. c 0
8
(x2 + 6x 4) sin4x dx .
6. c 0
2
cos2x sin5x dx .
7. c cc 1
12
dx
1 x2
.
8. c , y = x2 10x,
y = x2 + 4x . .
9. c , c Ox ,
y =3
x + 5, x = 4 x = 7 .
10. q TC(q),
q
MC = e2.9q, 92 .
. 97 300 2012/2013 .
-
MA , 3, 098
1. c dx7 6x .
2. c 3x2 + 6x 12
(x + 1)(x2 4x + 4)dx .
3. c 6 + x 9
x 9 + 4dx .
4. c 0
4
cos2x
sin22x + 9dx
5. c 12
12 3
arctg2x dx .
6. c 0
12
cos23x dx .
7. c cc 1
12
dx
1 x2
.
8. c , yx = 30, x + y = 11 .
.
9. c , c Ox ,
y = x2 + x y = 0 x [ 5, 4] .
10.
e t (t )
V(t) = 92 + 5 sin
4(t + 7)
. .
. 98 300 2012/2013 .
-
MA , 3, 099
1. c (8x 7) 4x2 7x 3 dx .
2. c 45(x2 + 2x + 8)
(x 6)(x2 + 9)dx .
3. c dxx 3 x3
.
4. c 0
12
cos6x
sin26x 9dx
5. c 0
4
(x2 + 7x + 7) sin2x dx .
6. c 0
18
sin26x dx .
7. c cc 1
12
dx
1 x2
.
8. c , y =36
x2 + 180,
y =1
216x2 . .
9. c , c Ox ,
y =7
x + 8, x = 8 x = 9 .
10. q TC(q),
q
MC = e1.4q, 65 .
. 99 300 2012/2013 .
-
MA , 3, 100
1. c dx1 7x .
2. c 15(x2 + 4x 1)
(x 2)(x + 1)(x + 3)dx .
3. c 4 + 3xx 2 + 1 dx .
4. c 16
112
ctg33x + 4 ctg3x + 3
sin23xdx .
5. c 12 3
0
arctg2x dx .
6. c 0
20
sin25x dx .
7. c cc 4
683 7 x 4
x 4dx
.
8. c , y = x2 8x 14,
y = x 4 . .
9. c , c Ox ,
y =9
x 3, x = 5 x = 2 .
10. q TC(q),
q
MC = e0.4q, 81 .
. 100 300 2012/2013 .
-
MA , 3, 101
1. c x dx6x
2 + 535
2. c 5(x2 8x + 3)
(x 2)(x2 2x + 5)dx .
3. c 7x 3x 1 1 dx .
4. c 18
112
ctg36x + 4 ctg26x 2
sin26xdx .
5. c 0
6
(x2 + x 4) sin3x dx .
6. c 0
16
sin24x dx .
7. c cc e73
e7
3dx
x7 + ln3x
.
8. c , yx = 3, x + y = 4 .
.
9. c , c Ox ,
y =6
x + 1, x = 6 x = 5 .
10. R(x), x
MR = 2x 210 .
. 101 300 2012/2013 .
-
MA , 3, 102
1. c (5 + x)43dx .
2. c 4(x2 + 6x 5)
(x + 6)(x2 + 12x + 40)dx .
3. c 4 + x 7
x + 18dx .
4. c ln2
ln6e2x
e4x + 4dx .
5. c 1
0
arctg x dx .
6. c 0
2
sin3x sin7x dx .
7. c cc 0
e2xdx
.
8. c , x + y = 7, yx = 10 .
.
9. c , c Ox ,
y =4
x + 5, x = 3 x = 4 .
10. V(t) ,
, 13% , . .
t V
V= 0 . 13t .
11 , , V(0) = 44 .
. 102 300 2012/2013 .
-
MA , 3, 103
1. c 14x + 47x2 + 4x + 7
dx .
2. c x2 + 6x + 8
(x 2)(x 1)(x 4)dx .
3. c x 1x + 1 1 dx .
4. c 0
8
cos4x
sin24x + 9dx
5. c 0
12
(x2 5x 5) sin6x dx .
6. c 0
2
cos3x sin6x dx .
7. c cc 7
8x 5 + 4 8 x
8 xdx
.
8. c , y =16
x2 + 96,
y =1
112x2 . .
9. c , c Ox ,
y = x2 4x y = 0 x [5, 6] .10. q TC(q),
q
MC = e0.8q, 37 .
. 103 300 2012/2013 .
-
MA , 3, 104
1. c (x + 4)36dx .
2. c x2 + 7x 4
x3 + x2dx .
3. c 8 xx + 6 + 1 dx .
4. c 38
14
3 ctg22x + ctg2x + 2
sin22xdx .
5. c 0
4
(x2 2x 6) cos2x dx .
6. c 0
24
cos26x dx .
7. c cc
sin7x dx
.
8. c , y = x2 + 4x 5,
y = 3x + 1 . .
9. c , c Ox ,
y = x2 + 7x y = 0 x [0, 3] .10.
MC(x) = 54 5x 4x2, 68 .
.
. 104 300 2012/2013 .
-
MA , 3, 105
1. c dx1 x2 arcsin x4
.
2. c 13(x2 + 4x + 5)
(x + 3)(x2 + 4)dx .
3. c x 2 + 1
x 18dx .
4. c 15
14
tg35x tg25x 2
cos25xdx .
5. c 0
6
(x2 + x + 4) cos3x dx .
6. c 0
12
sin26x dx .
7. c cc 12
cos2x dx
.
8. c , y =25
x2 + 125,
y =1
150x2 . .
9. c , c Ox ,
y =1
x + 8, x = 2 x = 3 .
10.
MC(x) = 73 8x 2x2, 77 .
.
. 105 300 2012/2013 .
-
MA , 3, 106
1. c dx1 5x .
2. c 5(x2 3x 6)
(x 2)(x2 6x + 13)dx .
3. c 6 x + 3
x + 3 + 4dx .
4. c ln3
ln4e3x
e6x 4dx .
5. c 0
6
(x2 5x 2) sin3x dx .
6. c 0
2
cos5x sin6x dx .
7. c cc 17
e8
7dx
x ln97x
.
8. c , y = 2x2 9x + 14,
y = 3x2 2x + 6 . .
9. c , c Ox ,
y = x2 9 y = 0 x [ 5, 4] .
10. ,
CM = 20q4 + 8q3 + 9q2, 160 .
. 106 300 2012/2013 .
-
MA , 3, 107
1. c 6x + 43x
2 + 4x 66dx .
2. c 5(x2 + x 5)
(x 2)(x2 6x + 13)dx .
3. c 7 + x + 8
x 1dx .
4. c 0
12
cos6x
sin26x + 9dx
5. c 1
4 3
14
arctg4x dx .
6. c 0
2
sin3x sin4x dx .
7. c cc 5
sin5x dx
.
8. c , yx = 72, x + y = 17 .
.
9. c , c Ox ,
y = x2 + 3x y = 0 x [0, 1] .10. V(t) ,
, 19% , . .
t V
V= 0 . 19t .
, 31 ,
, ,
V(0) = 68 .
. 107 300 2012/2013 .
-
MA , 3, 108
1. c 14x + 67x2 + 6x + 1
dx .
2. c 6(x2 7x 5)
x3 + 4x2 5xdx .
3. c x + 2 + 4
x + 6dx .
4. c 0
8
cos4x
sin24x + 4dx
5. c 0
4
(x2 4x + 7) sin2x dx .
6. c 0
2
sin4x sin7x dx .
7. c cc 8
dx
64 + x2
.
8. c , yx = 9, x + y = 10 .
.
9. c , c Ox ,
y =9
x + 2, x = 1 x = 3 .
10. R(x), x
MR = 7x3 170 .
. 108 300 2012/2013 .
-
MA , 3, 109
1. c x dx7x2 + 4
.
2. c 6(x2 2x + 6)
x3 9xdx .
3. c dxx2
3 + 5 x.
4. c 221
542
tg7x dx .
5. c 0
3
arctg x dx .
6. c 0
18
cos26x dx .
7. c cc 9
73 7 x 2
7 xdx
.
8. c , yx = 12, x + y = 7 .
.
9. c , c Ox ,
y = x2 1 y = 0 x [2, 3] .10. ,
CM = 18q5 + 6q2 + 6q , 460 .
. 109 300 2012/2013 .
-
MA , 3, 110
1. c dx7x 6 .
2. c 2(x2 8x + 5)
x3 3x2 + 2xdx .
3. c 7 x + 9
x + 9 + 9dx .
4. c 19
118
ctg3x dx .
5. c 0
4
(x2 7x 7) cos2x dx .
6. c 0
12
cos22x dx .
7. c cc
48
cos8x dx
.
8. c , y = x2 3x, y = 2x 4 .
.
9. c , c Ox ,
y =3
x 6, x = 7 x = 1 .
10. q TC(q),
q
MC = e0.8q, 51 .
. 110 300 2012/2013 .
-
MA , 3, 111
1. c dx1 4x .
2. c 15(x2 + 5x + 2)
(x + 7)(x + 2)(x 1)dx .
3. c x + 4x 6 + 1 dx .
4. c ln3
ln4e2x
e4x 77dx .
5. c 13
13 3
arctg3x dx .
6. c 0
2
sin4x sin6x dx .
7. c cc 8
7x 5
x + 8dx
.
8. c , x + y = 4, yx = 3 .
.
9. c , c Ox ,
y = x2 + x y = 0 x [ 3, 2] .
10.
MC(x) = 28 4x 6x2, 38 .
.
. 111 300 2012/2013 .
-
MA , 3, 112
1. c dx(x + 4)41 .
2. c 13(x2 5x + 9)
(x 3)(x2 + 4)dx .
3. c x 2 + 9
x + 14dx .
4. c 0
12
sin6x
cos26x 25dx
5. c 0
12
(x2 x 3) cos6x dx .
6. c 0
12
cos26x dx .
7. c cc 9 3
dx
81 + x2
.
8. c , yx = 10, x + y = 7 .
.
9. c , c Ox ,
y =5
x + 1, x = 6 x = 8 .
10. R(x), x
MR = 5x6 780 .
. 112 300 2012/2013 .
-
MA , 3, 113
1. c dx(3x + 1)77 .
2. c 5(x2 7x + 6)
(x 2)(x2 6x + 13)dx .
3. c 7 + x + 8
x 8dx .
4. c ln3
ln5e2x
e4x 16dx .
5. c 14
14
3
arctg4x dx .
6. c 0
42
sin27x dx .
7. c cc
4
sin2x dx
.
8. c , x + y = 7, yx = 10 .
.
9. c , c Ox ,
y = x2 + 3x y = 0 x [0, 3] .
10. ,
CM = 24q5 + 10q4 + 9q2, 840 .
. 113 300 2012/2013 .
-
MA , 3, 114
1. c dx(4 + x)22 .
2. c 13(x2 5x 4)
(x + 3)(x2 + 4)dx .
3. c 2x 7x + 7 + 1 dx .
4. c 0
6
sin3x
cos23x 25dx
5. c 13
0
arctg3x dx .
6. c 0
42
sin27x dx .
7. c cc
10
sin5x dx
.
8. c , y = x2 + 2x + 7,
y = 2x + 4 . .
9. c , c Ox ,
y =2
x 1, x = 5 x = 0 .
10. q TC(q),
q
MC = e5.2q, 74 .
. 114 300 2012/2013 .
-
MA , 3, 115
1. c x 5x2 + 7 dx .
2. c 15(x2 + 4x 9)
(x + 5)(x2 x 6)dx .
3. c x + 5 3
x 20dx .
4. c 514
1128
2 ctg37x ctg27x 5
sin27xdx .
5. c 0
10
(x2 + 2x + 1) sin5x dx .
6. c 0
12
cos24x dx .
7. c cc 1
0dx
1 x2
.
8. c , y = 10x2 12x 3,
y = 7x2 3x + 3 . .
9. c , c Ox ,
y =9
x 9, x = 3 x = 1 .
10. K(t),
( , )
I(t) = 300 t78 , K(0) = 380 .
. 115 300 2012/2013 .
-
MA , 3, 116
1. c (8x + 5) 4x2 + 5x + 46 dx .
2. c x2 + 4x 2
(x + 8)(x2 + 13x + 42)dx .
3. c x 3 + 2
x 19dx .
4. c 720
310
ctg35x + ctg25x 1
sin25xdx .
5. c 0
6
(x2 + 6x 7) cos3x dx .
6. c 0
12
sin24x dx .
7. c cc 0
dx
1 + x2
.
8. c , y = 4x2 + 4x + 3,
y = 2x2 + 12x + 13 . .
9. c , c Ox ,
y = x2 + 7x y = 0 x [0, 2] .
10.
e t (t )
V(t) = 23 + 8 cos
3(t + 4)
. .
. 116 300 2012/2013 .
-
MA , 3, 117
1. c 6x 53x
2 5x + 47dx .
2. c 12(x2 6x + 5)
x3 + x2 20xdx .
3. c x + 1 3
2 x + 1dx .
4. c 320
120
5 ctg25x 4 ctg5x + 4
sin25xdx .
5. c 0
12 3
arctg2x dx .
6. c 0
8
sin22x dx .
7. c cc 0
4x 3
4 xdx
.
8. c , y = 5x2 + 7x + 12,
y = 2x2 + 7x + 5 . .
9. c , c Ox ,
y = x2 + 5x y = 0 x [ 6, 5] .10. V(t) ,
, 28% , . .
t V
V= 0 . 28t .
, 22 a,
, ,
V(0) = 30 .
. 117 300 2012/2013 .
-
MA , 3, 118
1. c (12x + 5) 6x2 + 5x + 58 dx .
2. c x2 9x + 4
x3 + 3x2 + 2xdx .
3. c 1 + x 3
x 3 + 5dx .
4. c e2
e2
2dx
x ln82x.
5. c 0
12
(x2 x + 6) sin6x dx .
6. c 0
2
cos2x cos3x dx .
7. c cc e32
e5
2dx
x 3 + ln2x
.
8. c , y = 6x2,
y = 7x2 + 8x + 6 . .
9. c , c Ox ,
y = x2 36 y = 0 x [6, 7] .10. q TC(q),
q
MC = e9.8q, 12 .
. 118 300 2012/2013 .
-
MA , 3, 119
1. c 6x + 43x
2 + 4x 494
dx .
2. c x2 + 8x + 4
x3 x2dx .
3. c x 5x + 1 + 3 dx .
4. c e37
e5
7dx
x ln7x.
5. c 0
13
arctg3x dx .
6. c 0
6
sin22x dx .
7. c cc 1
0dx
1 x2
.
8. c , y = 5x2 + 4x + 6,
y = 4x2 + 3x + 4 . .
9. c , c Ox ,
y =6
x + 7, x = 2 x = 4 .
10. K(t),
( , )
I(t) = 550 t38 , K(0) = 860 .
. 119 300 2012/2013 .
-
MA , 3, 120
1. c x 6x2 + 723 dx .
2. c 85(x2 + x + 2)
(x + 9)(x2 + 4)dx .
3. c 4 xx + 5 2 dx .
4. c 0
8
cos4x
sin24x + 36dx
5. c 12 3
0
arctg2x dx .
6. c 0
12
cos23x dx .
7. c cc 3
676 7 x 3
x 3dx
.
8. c , y = x2 + 2x 5,
y = x 1 . .
9. c , c Ox ,
y = x2 x y = 0 x [4, 5] .
10.
e t (t )
V(t) = 38 + 4 sin
3(t + 4)
. .
. 120 300 2012/2013 .
-
MA , 3, 121
1. c arcsin9x
1 x2dx .
2. c 10(x2 + 2x + 4)
(x 1)(x2 + 9)dx .
3. c x + 2 + 8
x 23dx .
4. c ln2
ln5e2x
e4x 9dx .
5. c 0
13
arctg x dx .
6. c 0
2
cos7x cos6x dx .
7. c cc 0
dx
1 + x2
.
8. c , y = 8x2 + 3x 3,
y = 10x2 + 7x + 3 . .
9. c , c Ox ,
y = x2 4 y = 0 x [ 3, 2] .
10.
e t (t )
V(t) = 74 + 5 sin
6(t + 9)
. .
. 121 300 2012/2013 .
-
MA , 3, 122
1. c 6x 23x2 2x 5
dx .
2. c 5(x2 6x 6)
(x + 1)(x2 + 4)dx .
3. c x + 6 + 9
x + 2dx .
4. c 0
12
sin6x
cos26x + 49dx
5. c 0
4
(x2 6x 6) sin2x dx .
6. c 0
2
cos4x sin3x dx .
7. c cc
48
sin8x dx
.
8. c , y = x2 7,
y = 5x 1 . .
9. c , c Ox ,
y =4
x 3, x = 6 x = 9 .
10. V(t) ,
, 06% , . .
t V
V= 0 . 06t .
, 20 ,
, ,
V(0) = 45 .
. 122 300 2012/2013 .
-
MA , 3, 123
1. c dx6x 2 .
2. c 4(x2 + 3x + 4)
(x 2)(x2 4x + 8)dx .
3. c x + 8 2
x + 24dx .
4. c 34
78
5 ctg32x + 2 ctg2x + 3
sin22xdx .
5. c 13 3
0
arctg3x dx .
6. c 0
15
cos25x dx .
7. c cc 8
sin4x dx
.
8. c , x + y = 11, yx = 30 .
.
9. c , c Ox ,
y =4
x + 8, x = 4 x = 6 .
10. q TC(q),
q
MC = e0.2q, 52 .
. 123 300 2012/2013 .
-
MA , 3, 124
1. c 10x 45x
2 4x 516
dx .
2. c x2 5x 2
x3 xdx .
3. c 9 x3
5 8 x23
dx .
4. c ln4
ln3e2x
9 25e4xdx .
5. c 0
14
3
arctg4x dx .
6. c 0
2
cos3x sin6x dx .
7. c cc 0
1x 6
1 xdx
.
8. c , y =4
x2 + 4, y =
1
8x2 .
.
9. c , c Ox ,
y = x2 1 y = 0 x [ 3, 1] .10. ,
CM = 20q4 + 9q2 + 8q , 670 .
. 124 300 2012/2013 .
-
MA , 3, 125
1. c (6x 4) 3x2 4x 56 dx .
2. c 6(x2 + 5x 2)
(x + 7)(x2 4x 5)dx .
3. c 5 + x 3
x 28dx .
4. c 0
8
sin4x
cos24x 4dx
5. c 13
3
13
arctg3x dx .
6. c 0
4
sin22x dx .
7. c cc
24
sin4x dx
.
8. c , y = 4x2 + 10x 1,
y = 3x2 + 3x 1 . .
9. c , c Ox ,
y = x2 x y = 0 x [ 3, 2] .
10.
MC(x) = 13 4x 3x2, 96 .
.
. 125 300 2012/2013 .
-
MA , 3, 126
1. c dx(3x + 2)89 .
2. c 2x2 + 12x + 2
(x + 1)(x2 + 6x + 9)dx .
3. c 9 x
7 2 x34
dx .
4. c 58
1116
ctg34x + 3 ctg4x + 2
sin24xdx .
5. c 0
8
(x2 + 4x 1) sin4x dx .
6. c 0
2
sin3x sin6x dx .
7. c cc 0
cos2x dx
.
8. c , yx = 8, x + y = 9 .
.
9. c , c Ox ,
y = x2 8x y = 0 x [ 2, 1] .
10. V(t) ,
, 44% , . .
t V
V= 0 . 44t .
, 14 ,
, ,
V(0) = 88 .
. 126 300 2012/2013 .
-
MA , 3, 127
1. c dx(3x 5)32 .
2. c 13(x2 + x + 5)
x3 4x2 + 13xdx .
3. c 1 x + 1
x + 1 + 4dx .
4. c 58
34
ctg32x 3 ctg22x 3
sin22xdx .
5. c 0
8
(x2 + 2x 1) sin4x dx .
6. c 0
2
cos3x cos4x dx .
7. c cc 3
4dx
(x 2) ln(x 2)
.
8. c , y = x2 + 6x + 8,
y = x 4 . .
9. c , c Ox ,
y =9
x + 3, x = 0 x = 4 .
10. e
z(t) = 65t 7 . 74t2 , t ( ), .
C 7 . 13
, 92 .
. 127 300 2012/2013 .
-
MA , 3, 128
1. c dx4 8x .
2. c 45(x2 + x + 5)
(x + 6)(x2 + 9)dx .
3. c dxx2
3 + x.
4. c 516
38
3 ctg34x 3 ctg4x + 4
sin24xdx .
5. c 13
3
0
arctg3x dx .
6. c 0
15
cos25x dx .
7. c cc 1
dx
1 + x2
.
8. c , x + y = 7, yx = 10 .
.
9. c , c Ox ,
y = x2 + 5x y = 0 x [0, 1] .
10. K(t),
( , )
I(t) = 80(t 1)78 , ( t = 1)
560 .
. 128 300 2012/2013 .
-
MA , 3, 129
1. c (x + 4)55dx .
2. c 2(x2 + 6x + 4)
x3 xdx .
3. c x 7 + 2
6 + x 7dx .
4. c ln2
ln3e3x
e6x 36dx .
5. c 1
3
arctg x dx .
6. c 0
2
sin7x sin5x dx .
7. c cc 1
1dx
1 x2
.
8. c , yx = 15, x + y = 8 .
.
9. c , c Ox ,
y =6
x + 8, x = 6 x = 5 .
10. ,
: z(t) = 0 . 736t2 + 5 . 8t + 7 . 4 t
( ), .
. 129 300 2012/2013 .
-
MA , 3, 130
1. c arctg x1 + x2 dx .
2. c 5(x2 + 2x + 1)
(x + 4)(x2 + 6x + 13)dx .
3. c 2x 7x + 1 1 dx .
4. c ln2
ln6e2x
e4x + 4dx .
5. c 0
6
(x2 + 5x 5) cos3x dx .
6. c 0
2
sin4x sin6x dx .
7. c cc 36
cos6x dx
.
8. c , y = 8x2 8x + 1,
y = 7x2 3x + 7 . .
9. c , c Ox ,
y =9
x + 2, x = 3 x = 6 .
10. ,
CM = 12q3 + 6q2 + 6q , 540 .
. 130 300 2012/2013 .
-
MA , 3, 131
1. c dx7 5x .
2. c 5(x2 + x + 2)
(x + 3)(x2 + 4x + 8)dx .
3. c 8 + x 4
x + 5dx .
4. c 34
12
5 ctg3x + 3 ctg2x 4
sin2xdx .
5. c 0
6
(x2 + 5x 1) sin3x dx .
6. c 0
2
cos2x sin3x dx .
7. c cc e34
e3
4dx
x3 + ln4x
85
.
8. c , y = x2 + 5x + 11,
y = 3x + 3 . .
9. c , c Ox ,
y = x2 1 y = 0 x [ 4, 1] .
10.
MC(x) = 16 5x 4x2, 62 .
.
. 131 300 2012/2013 .
-
MA , 3, 132
1. c dx7 2x .
2. c 29(x2 x + 3)
(x + 3)(x2 4x + 8)dx .
3. c dxx + x3
.
4. c 38
14
4 ctg22x 4 ctg2x 1
sin22xdx .
5. c 0
6
(x2 x + 6) sin3x dx .
6. c 0
2
cos5x sin6x dx .
7. c cc 4
cos2x dx
.
8. c , y =49
x2 + 343,
y =1
392x2 . .
9. c , c Ox ,
y = x2 + x y = 0 x [ 4, 3] .
10. R(x), x
MR = x8 820 .
. 132 300 2012/2013 .
-
MA , 3, 133
1. c dx4x + 1 .
2. c 10(x2 x + 7)
x3 + 2x2 + 10xdx .
3. c 2x 1x 3 1 dx .
4. c ln3
ln4e3x
e6x 25dx .
5. c 0
12
3
arctg2x dx .
6. c 0
2
cos6x sin7x dx .
7. c cc 6
sin3x dx
.
8. c , x + y = 11, yx = 24 .
.
9. c , c Ox ,
y = x2 + 5x y = 0 x [ 7, 6] .10. R(x), x
MR = 8x3 950 .
. 133 300 2012/2013 .
-
MA , 3, 134
1. c dx2x + 4 .
2. c x2 + x + 4
(x + 8)(x2 + 9x + 20)dx .
3. c 4x 5x + 1 1 dx .
4. c ln3
ln4e3x
e6x + 9dx .
5. c 0
12
(x2 5x 2) cos6x dx .
6. c 0
6
sin23x dx .
7. c cc 5
413 + 5 x 5
x 5dx
.
8. c , yx = 21, x + y = 10 .
.
9. c , c Ox ,
y =3
x + 3, x = 2 x = 6 .
10.
MC(x) = 40 8x x2, 56 .
.
. 134 300 2012/2013 .
-
MA , 3, 135
1. c dx5x + 4 .
2. c x2 + 5x 8
(x 2)(x2 8x + 15)dx .
3. c x + 2 + 6
1 + x + 2dx .
4. c 14
18
2 ctg32x 4 ctg22x 1
sin22xdx .
5. c 12
3
0
arctg2x dx .
6. c 0
6
cos22x dx .
7. c cc 12
1dx
1 x2
.
8. c , y = x2 + 11,
y = x 1 . .
9. c , c Ox ,
y = x2 16 y = 0 x [ 5, 4] .
10. ()
8 20
f (t) = 5000 + 68t 3t2, t , 8 t 20.
, 16 17 ,
1 6 . .
. 135 300 2012/2013 .
-
MA , 3, 136
1. c x dx7x2 4 .
2. c 8(x2 + x 6)
x3 4x2 + 8xdx .
3. c 9 + x + 1
x + 10dx .
4. c ln3
ln2e2x
36 25e4xdx .
5. c 0
10
(x2 5x 3) cos5x dx .
6. c 0
18
sin26x dx .
7. c cc 4
dx
16 + x2
.
8. c , y = 5x2 + 3x,
y = 3x2 + 3x + 8 . .
9. c , c Ox ,
y =3
x 6, x = 9 x = 1 .
10. ,
CM = 12q5 + 15q4 + 9q2, 950 .
. 136 300 2012/2013 .
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MA , 3, 137
1. c (12x 5) 6x2 5x 595 dx .
2. c 9(x2 + 3x 8)
(x 2)(x2 + 4x 21)dx .
3. c dxx 3 x3
.
4. c 14
518
tg3x dx .
5. c 13
3
0
arctg3x dx .
6. c 0
14
cos27x dx .
7. c cc 4
sin2x dx
.
8. c , y =16
x2 + 112,
y =1
128x2 . .
9. c , c Ox ,
y = x2 + 2x y = 0 x [ 5, 3] .10. V(t) ,
, 0 . 16, . .
t V
V= 0 . 16t .
11 , , V(0) = 67 .
. 137 300 2012/2013 .
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MA , 3, 138
1. c 6x 53x
2 5x 412
dx .
2. c x2 + 8x + 2
x3 + x2dx .
3. c x 8x + 2 3 dx .
4. c ln2
ln4e2x
e4x + 65dx .
5. c 0
6
(x2 2x + 4) sin3x dx .
6. c 0
2
cos3x sin2x dx .
7. c cc 1
1dx
1 x2
.
8. c , y = x2 + 3x + 5,
y = 2x + 1 . .
9. c , c Ox ,
y =7
x 6, x = 2 x = 1 .
10. V(t) ,
, 0 . 03, . .
t V
V= 0 . 03t .
20 , , V(0) = 71 .
. 138 300 2012/2013 .
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MA , 3, 139
1. c dx8x + 3 .
2. c 5(x2 + x 8)
(x 2)(x2 6x + 13)dx .
3. c 9 + x 1
x 37dx .
4. c ln5
ln6e2x
e4x + 25dx .
5. c 1
3 3
13
arctg3x dx .
6. c 0
2
cos4x sin5x dx .
7. c cc 18
e3
8dx
x ln4(8x)
.
8. c , yx = 56, x + y = 15 .
.
9. c , c Ox ,
y =4
x 3, x = 4 x = 2 .
10. R(x), x
MR = 5x2 710 .
. 139 300 2012/2013 .
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MA , 3, 140
1. c dx1 5x .
2. c 6(x2 2x + 7)
x3 5x2 14xdx .
3. c x 3 + 7
x + 6dx .
4. c ln3
ln4e3x
e6x 25dx .
5. c 1
13
arctg x dx .
6. c 0
18
cos26x dx .
7. c cc
12
cos2x dx
.
8. c , yx = 24, x + y = 11 .
.
9. c , c Ox ,
y = x2 5x y = 0 x [ 3, 0] .10. K(t),
( , )
I(t) = 600 t75 , K(0) = 740 .
. 140 300 2012/2013 .
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MA , 3, 141
1. c (6x + 5) 3x2 + 5x + 69 dx .
2. c 10(x2 4x + 7)
x3 2x2 + 10xdx .
3. c dxx2
3 + x.
4. c 32
74
5 ctg3x 2 ctg2x + 3
sin2xdx .
5. c 0
13
arctg3x dx .
6. c 0
24
cos26x dx .
7. c cc 0
e2xdx
.
8. c , yx = 56, x + y = 15 .
.
9. c , c Ox ,
y = x2 x y = 0 x [1, 3] .10. R(x), x
MR = 9x 160 .
. 141 300 2012/2013 .
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MA , 3, 142
1. c dx(5x 3)26 .
2. c x2 3x + 2
(x 3)(x2 8x + 16)dx .
3. c dxx2
3 + 5 x.
4. c 38
14
3 ctg32x + 5 ctg22x 3
sin22xdx .
5. c 0
12
(x2 2x 1) cos6x dx .
6. c 0
2
sin5x sin6x dx .
7. c cc 3
1x + 3
1 xdx
.
8. c , y = 5x2 + 7x 3,
y = 3x2 5x + 11 . .
9. c , c Ox ,
y = x2 5x y = 0 x [ 3, 0] .
10. V(t) ,
, 0 . 03, . .
t V
V= 0 . 03t .
, 20 ,
, ,
V(0) = 49 .
. 142 300 2012/2013 .
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MA , 3, 143
1. c x 2x2 + 756 dx .
2. c 9(x2 + 2x + 5)
(x + 3)(x2 + 6x + 18)dx .
3. c x 5x + 4 1 dx .
4. c 0
112
tg33x 4 tg23x + 4
cos23xdx .
5. c 0
12
(x2 3x + 6) cos6x dx .
6. c 0
2
cos3x sin5x dx .
7. c cc
5
cos5x dx
.
8. c , y =49
x2 + 245,
y =1
294x2 . .
9. c , c Ox ,
y =2
x + 5, x = 3 x = 2 .
10. K(t),
( , )
I(t) = 260(t 1)58 , K(1) = 250 .
. 143 300 2012/2013 .
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MA , 3, 144
1. c (2x 3) x2 3x 4 dx .
2. c x2 5x + 3
(x 5)(x2 12x + 36)dx .
3. c 6 xx 1 3 dx .
4. c ln2
ln3e2x
e4x + 20dx .
5. c 0
12
(x2 + x + 1) sin6x dx .
6. c 0
2
cos5x sin3x dx .
7. c cc 1
12
dx
1 x2
.
8. c , y = 6x2 7x 6,
y = 7x2 + x 6 . .
9. c , c Ox ,
y = x2 + 3x y = 0 x [ 6, 5] .
10. e
z(t) = 35t 3 . 39t2 , t ( ), .
C 8 . 22
, 90 .
. 144 300 2012/2013 .
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MA , 3, 145
1. c 8x 54x2 5x + 56
dx .
2. c x2 + x + 4
x2 x3dx .
3. c dxx x3
.
4. c ln4
ln2e2x
25 81e4xdx .
5. c 0
4
(x2 4x + 1) cos2x dx .
6. c 0
12
cos23x dx .
7. c cc
24
sin4x dx
.
8. c , yx = 6, x + y = 5 .
.
9. c , c Ox ,
y =3
x 9, x = 6 x = 8 .
10. ,
: z(t) = 0 . 954t2 + 8 . 1t + 8 . 1 t
( ), .
. 145 300 2012/2013 .
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MA , 3, 146
1. c dx3x + 2 .
2. c 8(x2 x 5)
(x + 1)(x2 2x + 5)dx .
3. c x + 6 9
x 10dx .
4. c 0
6
cos3x
sin23x + 36dx
5. c 1
13
arctg x dx .
6. c 0
2
cos3x sin6x dx .
7. c cc
cos8x dx
.
8. c , yx = 18, x + y = 11 .
.
9. c , c Ox ,
y =1
x 2, x = 5 x = 8 .
10.
e t (t )
V(t) = 26 + cos
6(t + 1)
. .
. 146 300 2012/2013 .
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MA , 3, 147
1. c arcsin2x
1 x2dx .
2. c 8(x2 + 2x + 3)
x3 + 4x2 + 8xdx .
3. c 2x 7x + 3 + 1 dx .
4. c 0
10
sin5x
cos25x 25dx
5. c 0
12
(x2 + 6x + 5) sin6x dx .
6. c 0
21
sin27x dx .
7. c cc 0
e4xdx
.
8. c , y = x2 + 2x, y = 4x + 3 .
.
9. c , c Ox ,
y =7
x 8, x = 4 x = 1 .
10. R(x), x
MR = 3x8 340 .
. 147 300 2012/2013 .
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MA , 3, 148
1. c dx(4x 5)105 .
2. c x2 7x 5
(x 7)(x2 12x + 36)dx .
3. c x 9 + 6
x 45dx .
4. c 14
512
3 tg33x tg23x + 4
cos23xdx .
5. c 12
3
0
arctg2x dx .
6. c 0
16
cos24x dx .
7. c cc
35
55x+2 dx
.
8. c , y = 4x2 5x + 7,
y = 6x2 x + 7 . .
9. c , c Ox ,
y =2
x + 8, x = 1 x = 5 .
10. V(t) ,
, 22% , . .
t V
V= 0 . 22t .
, 12 ,
, ,
V(0) = 88 .
. 148 300 2012/2013 .
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MA , 3, 149
1. c arcsin x1 x2
dx .
2. c 3(x2 + 2x + 7)
(x + 9)(x 6)(x 5)dx .
3. c x 6 + 4
1 x 6dx .
4. c 0
6
cos3x
sin23x + 36dx
5. c 0
6
(x2 + 7x 4) cos3x dx .
6. c 0
8
sin24x dx .
7. c cc 14
+
54x1 dx
.
8. c , y = 2x2 2x 5,
y = 9x2 2x + 2 . .
9. c , c Ox ,
y = x2 3x y = 0 x [ 2, 0] .
10. ,
: z(t) = 0 . 811t2 + 5 . 7t + 4 . 8 t
( ), .
. 149 300 2012/2013 .
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MA , 3, 150
1. c x dx3x2 + 5
.
2. c 8(x2 + 8x 3)
(x 2)(x2 + 4)dx .
3. c x + 4 3
1 + x + 4dx .
4. c 16
15
tg5x dx .
5. c 0
8
(x2 7x 1) sin4x dx .
6. c 0
6
sin22x dx .
7. c cc 12
cos6x dx
.
8. c , yx = 28, x + y = 11 .
.
9. c , c Ox ,
y = x2 8x y = 0 x [ 4, 3] .
10.
MC(x) = 48 7x 4x2, 59 .
.
. 150 300 2012/2013 .
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MA , 3, 151
1. c 90x dx( 4x2 + 7)91
.
2. c 4(x2 + 4x + 1)
(x + 3)(x2 + 6x + 13)dx .
3. c 1 + x + 2
x 7dx .
4. c 0
14
cos7x
sin27x + 16dx
5. c 1
3
1
arctg x dx .
6. c 0
12
sin24x dx .
7. c cc 6 3
dx
36 + x2
.
8. c , y = x2 + x,
y = 2x 2 . .
9. c , c Ox ,
y =5
x + 5, x = 3 x = 0 .
10. ()
8 20
f (t) = 6000 + 85t 3t2, t , 8 t 20.
, 10 14 ,
1 4 . .
. 151 300 2012/2013 .
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MA , 3, 152
1. c x dx7x2 4 .
2. c 13(x2 2x 1)
(x + 4)(x2 + 2x + 5)dx .
3. c 2x 7x