cong thuc va bai tap nguyen ham va tich phan
TRANSCRIPT
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7/23/2019 Cong Thuc Va Bai Tap Nguyen Ham Va Tich Phan
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NGUYN HM V TCH PHN Ti liu: V An Th
CC CNG THC HM! NGUYN HM
"# $%n& '() h* +,+ h* -. -/ +01 +/ 2%n:
1/ ( )c ' 0= (c l hng s) 2/ ( )m m 1x ' mx -= 3/ ( )sinx ' cosx=
4/ ( )cosx ' sinx= - 5/ ( ) 2
1tanx '
cos x
= 6/ ( ) 2
1cotx '
sin x
= -
7/ ( )x xa ' a lna= 8/ ( )x xe ' e= 9/ ( ) 1
lnx 'x
=
3# C,+ n&u45n h* +/ 2%n:
( )1 dx x c= + ( ) ( )n 1
n x2 x dx c n 1n 1
+
= + -+
( ) dx
3 ln x cx
= + ( ) dx 1
3' ln ax b cax b a
= + ++
( ) x x4 e dx e c= + ( ) ax b ax b1
4' e dx e ca
+ += + ( )a 0
( )x
x a5 a dx clna
= +
( )6 sinxdx cosx c= - + ( ) ( ) ( )1
6' sin ax b dx cos ax b ca
+ = - + +
( )7 cosxdx sinx c= + ( ) ( ) ( )1
7' cos ax b dx sin ax b ca
+ = + +
( ) 2dx8 tanx ccos x= + ( ) 2dx9 cotx csin x = - +
( )10 tanxdx ln cosx c= - + ( )10' cotxdx ln sinx c= +
( ) 2
dx 1 x 111 ln c
2 x 1x 1
-= +
+- ( ) 2 2dx 1 x a
11' ln c2a x ax a
-= +
+-
( ) 22
dx12 ln x x c
x = + + +
+
( ) 2 2 2x 1
13 x 1dx x 1 ln x x 1 c2 2+ = + + + + +( ) 2 2 2
x 14 x dx x ln x x c
2 2+ = + + + + +
6# T7nh +h08:1! ( ) ( )
2! ( ) ( ) ( ) ( )
kf x dx k f x dx
f x g x dx f x dx g x dx
=
=
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NGUYN HM V TCH PHN Ti liu: V An ThA9: T* n&u45n h* +;< +,+ h* -. 2=n& '>nh n&h?
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7/23/2019 Cong Thuc Va Bai Tap Nguyen Ham Va Tich Phan
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NGUYN HM V TCH PHN Ti liu: V An Th"#Ph/n& 1h,1 'i 2iEn -.#
T,nh - = dxxuxuf )()/.(0 ng cch & & = (x)1. & & = (x) dxxudt )(=2. - =
= dttfdxxuxuf )()()/.(0
T* n&u45n h* +;< +,+ h* -. -
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NGUYN HM V TCH PHN Ti liu: V An Th
TCH PHN"# >nh n&h?& ng?
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7/23/2019 Cong Thuc Va Bai Tap Nguyen Ham Va Tich Phan
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NGUYN HM V TCH PHN Ti liu: V An Th
$i "# TNH TCH PHN $QNG CCH R 9SNG TNH CHT V NGUYN HM CK $N:
1.1
3
%
( 1)x x dx+ + 2! 2
2
1
1 1( )
e
x x dxx x
+ + + 3!2
1
1x dx+
4!2
3
(2 s$n 3 )x cosx x dx
+ + 5!1
%
( )xe x dx+ 6!1
3
%
( )x x x dx+
7!2
1
( 1)( 1)x x x dx+ + #2
3
1(3s$n 2 )x cosx dx
x
+ + 9!1
2
%
( 1)xe x dx+ +
10!2
2 3
1
( )x x x x dx+ + 11!2
1
( 1)( 1)x x x dx + + 12!3
3
1
x 1 Lx( )!
+
13.2
2
2
-1
x!dx
x + 14.2
1
7x 2 x 5Lx
x
15.
x 2
5
2
dx
x 2+ +
16.
2
2
1
x 1 Lx
x x x
( )!
ln
++ 17.
2 3
3
6
x Lx
x
cos !
sin
18.
4
2
%
&gx Lx
x
!
cos
19.
1 x x
x x
%
dx
+ 2%.
1 x
x x%
Lx
!+
21.2
21
Lx
4x 8x+
22.3
x x
%
Lx
ln!
+
22.2
%
Lx
1 xsin
+
24.
++1
1
2 )12( dxxx
25. 2
%
3)
3
22( dxxx 26.
2
2
)3( dxxx 27.
4
3
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28. dxxx
+
2
1
32
11 29.
2
1
3
2 2dx
x
xx 3%.
e
e
x
dx
1
1
31. 16
1
.dxx 32. dxx
xxe
+
2
1
752 33. dx
xx
8
13 2
3
14
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NGUYN HM V TCH PHN Ti liu: V An Th
$W 3: PHJKNG PHP XW $WN:
1!2
3 2
3
s$n xcos xdx
2!2
2 3
3
s$n xcos xdx
3!2
%
s$n
1 3
xdx
cosx
+
3!4
%
tgxdx
4!4
6
c'&gxdx
5!6
%
1 4s$nxcosxdx
+
6!
1
2
%
1x x dx+
7!
1
2
%
1x x dx
8!
1
3 2
%
1x x dx+
9!
1 2
3% 1
xdx
x +
1%.1
3 2
%
1x x dx
11.2
31
1
1dx
x x +
12.1
2
%
1
1 dxx+
13.1
2
1
1
2 2dx
x x + +
14.1
2%
1
1dx
x +
15.1
2 2
%
1
(1 3 ) dx
x+
16.2
s$n
4
xe cosxdx
17.2
4
s$ncosxe xdx
18!2
1
2
%
xe xdx+
19!2
3 2
3
s$n xcos xdx
20!2
s$n
4
xe cosxdx
21!2
4
s$ncosxe xdx
22!2
1
2
%
xe xdx+
23.2
3 2
3
s$n xcos xdx
24.2
2 3
3
s$n xcos xdx
25.2
%
s$n
1 3
xdx
cosx
+
26.4
%
tgxdx
27.4
6
c'&gxdx
28.6
%
1 4s$nxcosxdx
+
29.1
2
%
1x x dx+
30!
1
2
%
1x x dx
31!
1
3 2
%
1x x dx+
32!
1 2
3% 1
xdx
x +
33!
1
3 2
%
1x x dx
34!2
31
1
1dx
x x +
35!1
1 lne xdx
x
+
36!1
s$n(ln )e xdx
x
37!1
1 3ln lne x xdx
x
+
38!2 ln 1
1
e xedx
x
+
39!
2
21 lnln
e
e
x dxx x+
40!
2
2
1
(1 ln )
e
e
dxcos x+ 41!
2
1 1 1
xdx
x+
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NGUYN HM V TCH PHN Ti liu: V An Th
42!
1
% 2 1
xdx
x +
43!
1
%
1x x dx+
44!
1
%
1
1
dx
x x+ +
45!
1
%
1
1 dx
x x+
46!3
1
1xdx
x
+
47.1
1 lne xdx
x
+
48!
1
s$n(ln )e xdx
x
49!1
1 3ln lne x xdx
x
+
50!2 ln 1
1
e xedx
x
+
51!
221 ln
ln
e
e
xdx
x x
+
52!
1
2 3
%
5+
x x dx
53. ( )2
4
%
s$n 1 c's
+ x xdx
54.
4
2
%
4 x dx
55.
4
2
%
4 x dx56.
1
2
%1
dx
x+
57. dxe x
+%
1
32
58.
1
%
dxe x
59.1
3
0
xdx
(2x 1)+
6%.1
0
xdx
2x 1+
61.1
0
x 1 xdx
62.1
2
0
4x 11dx
x 5x 6
+
+ +
63.1
2
0
2x 5dx
x 4x 4
+
64.3 3
2
0
xdx
x 2x 1+ +
65.6
6 6
0
(sin x cos x)dx
+
66. 32
0
4sin xdx
1 cosx
+
67.4
2
0
1 sin2xdx
cos x
+ 68.
24
0
cos 2xdx
69.2
6
1 sin2x cos2xdx
sinx cosx
+ +
+
7%.1
x
0
1dx
e 1+ .
71. dxxx )s$n(c's
4
%
44
72. +
4
% 2s$n21
2c's
dxx
x
73. +
2
% 13c's2
3s$n
dxx
x
74.
2
% s$n25
c's
dxx
x
75.
75. +
+%
2
2 32
22 dx
xx
x
76. ++
1
12 52xx
dx
77.2
3 2
0
cos xsin xdx
78.2
5
0
cos xdx
79.4
20
sin4xdx
1 cos x
+8%.
1
3 2
0
x 1 x dx
81.2
2 3
0
sin2x(1 sin x) dx
+
82.4
4
0
1dx
cos x
83.e
1
1 lnxdxx
+
84.4
0
1dx
cosx
85.e 2
1
1 ln xdx
x
+ 86.
1
5 3 6
0
x (1 x ) dx
87.6
2
0
cosxdx
6 5sinx sin x
+
88.3 4
0
t xdx
cos2x
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NGUYN HM V TCH PHN Ti liu: V An Th
$i 6: PHJKNG PHP TCH PHN TZNG PH[N:
1.3
3
1
lne
xdx
x
2.1
ln
e
x xdx
3.
1
2
%
ln( 1)x x dx+
4.2
1
ln
e
x xdx
5.3
3
1
lne
xdx
x
6.1
ln
e
x xdx7.
1
2
%
ln( 1)x x dx+
8.2
1
ln
e
x xdx
9.2
%
( 'sx)s $nxx c dx
+
1%.1
1( ) ln
e
x xdxx
+
11.
2
2
1
ln( )x x dx+
12.3
2
4
&anx xdx
13. 3
2
2 )ln( dxxx
14.2
%
c'sx xdx
15.
1
%
xxe dx
16. +2
%
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xdxxx
17. 1
%
3. dxex x
18. 2
%
c's)1(
xdxx
19. 6
%
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xdxx
2%. 2
%
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ln
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26.
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x
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45. e
dxx
x
1
ln
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