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TUYN TP TCH PHN (P N CHI TIT)
BIN SON: LU HUY THNG
Ton b ti liu ca thy trang: http://www.Luuhuythuong.blogspot.com
H NI, 4/2014
H V TN:
LP :.
TRNG :

GV. Lu Huy Thng 0968.393.899
B HC V B - CHUYN CN S N BN Page 1
TCH PHN C BN
Ton b ti liu luyn thi i hc mn ton ca thy Lu Huy Thng:
http://www.Luuhuythuong.blogspot.com
HT 1.Tnh cc tch phn sau:
a)
13
1
0
I x dx= b) 1
32
0
(2 1)I x dx= + c) 1
33
0
(1 4 )I x dx=
d)
12 3
4
0
( 1)( 2 5)I x x x dx= + e) 1
2 35
0
(2 3)( 3 1)I x x x dx= +
Bi gii
a)
1 43 1
1 0
0
1
4 4
xI x dx= = =
b)
13
2
0
(2 1)I x dx= + Ch : 1
(2 1) 2 (2 1)2
d x dx dx d x+ = = +
1 1 43 3 1
2 0
0 0
(2 1)1 1 81 1(2 1) (2 1) (2 1) 10
2 2 4 8 8
xI x dx x d x
+ = + = + + = = =
c)
13
3
0
(1 4 )I x dx= Ch : 1
(1 4 ) 4 (1 4 )4
d x dx dx d x = =
1 1 43 3 1
3 0
0 0
(1 4 )1 1 81 1(1 4 ) (1 4 ) (1 4 ) 5
4 4 4 16 16
xI x dx x d x
= = = = + =
d)
12 3
4
0
( 1)( 2 5)I x x x dx= + Ch : 2 21
( 2 5) (2 2) ( 1) ( 2 5)2
d x x x dx x dx d x x + = = +
1 12 3 2 3 2
4
0 0
1( 1)( 2 5) ( 2 5) ( 2 5)
2I x x x dx x x d x x = + = + +
2 410
( 2 5)1 615 671. 1622 4 8 8
x x += = =

GV. Lu Huy Thng 0968.393.899
e)
12 3
5
0
(2 3)( 3 1)I x x x dx= + Ch : 2( 3 1) (2 3)d x x x dx + =
1 1
2 3 2 3 25
0 0
(2 3)( 3 1) ( 3 1) ( 3 1)I x x x dx x x d x x = + = + +
2 410
( 3 1) 1 10
4 4 4
x x += = =
a)
1
1
0
I xdx= b) 7
2
2
2I x dx= + c) 4
3
0
2 1I x dx= +
d)
12
4
0
1I x x dx= + e) 1
25
0
1I x x dx= f) 1
26
0
(1 ) 2 3I x x x dx= +
g)
12 3
7
0
1I x x dx= + h)1
2 3 28
0
( 2 ) 3 2I x x x x dx= +
Bi gii
a)
1
1
0
I xdx= 102 2
3 3x x= =
b)
7
72 2
2
2 16 382 ( 2) 2 18
3 3 3I x dx x x= + = + + = =
c)
4
3
0
2 1I x dx= +4
40
0
1 1 2 1 262 1 (2 1) . (2 1) 2 1 9
2 2 3 3 3x d x x x= + + = + + = =
d)
1 1
2 2 2 2 2 14 0
0 0
1 1 2 2 2 11 1 (1 ) . (1 ) 1
2 2 3 3 3I x x dx x d x x x= + = + + = + + =
e)
1
25
0
1I x x dx= 1
2 2 2 2 10
0
1 1 2 1 11 (1 ) . (1 ) 1 0
2 2 3 3 3x d x x x= = = + =
f)
1 1
2 2 26
0 0
1(1 ) 2 3 2 3 ( 2 3)
2I x x x dx x x d x x= + = + +
2 2 10
1 2 2 2. ( 2 3) 2 3 32 3 3
x x x x= + + = +

GV. Lu Huy Thng 0968.393.899
g)
1 12 3 3 3 3 3 1
7 0
0 0
1 1 2 4 2 21 1 ( 1) . ( 1) 1
3 3 3 9I x x dx x d x x x
= + = + + = + + =
h)
1 12 3 2 3 2 3 2
8
0 0
1( 2 ) 3 2 3 2 ( 3 2)
3I x x x x dx x x d x x= + = + +
3 2 3 2 10
1 2 4 2 4 2. ( 3 2) 3 2 03 3 9 9
x x x x= + + = =
a)
4
1
1
dxI
x
= b) 1
2
02 1
dxI
x
=+ c)
0
3
11 2
dxI
x
=
d)
1
42
0
( 1)
2 2
x dxI
x x
+=
+ + e)
1
52
0
( 2)
4 5
x dxI
x x
=
+
Bi gii
a)
44
1 1
1
2 4 2 2dx
I x
x
= = = =
b)
1 11
2 0
0 0
(2 1)12 1 3 1
22 1 2 1
d xdxI x
x x
+= = = + =
+ +
c)
0 00
3 1
1 1
(1 2 )11 2 1 3
21 2 1 2
d xdxI x
x x
= = = = +
d)
1 1 22 1
4 02 2
0 0
( 1) ( 2 2)12 2 5 2
22 2 2 2
x dx d x xI x x
x x x x
+ + += = = + + =
+ + + +
e)
1 1 22 1
5 02 2
0 0
( 2) ( 4 5)14 5 2 5
24 5 4 5
x dx d x xI x x
x x x x
+= = = + =
+ +
a) 11
e
dxI
x= b)
0
2
11 2
dxI
x
= c)
1
3 20
1
xdxI
x
=+
d)
1
4 20
( 1)
2 2
x dxI
x x
+=
+ + e)
1
5 20
2
4 5
xI dx
x x
=
+
Bi gii

GV. Lu Huy Thng 0968.393.899
a) 1 11
ln ln ln1 1
e
edxI x e
x= = = =
b)
0
2
11 2
dxI
x
=
001
1
(1 2 )1 1 1 ln 3ln 1 2 (ln1 ln 3)
2 1 2 2 2 2
d xx
x
= = = =
c)
1
3 20
1
xdxI
x
=+
( )21
2 102
0
11 1 1 ln2
ln 1 (ln2 ln1)2 2 2 21
d x
x
x
+= = + = =
+
d)
1
4 20
( 1)
2 2
x dxI
x x
+=
+ +
1 2
20
( 2 2)1
2 2 2
d x x
x x
+ +=
+ + 2 10
1 1 1 5ln 2 2 (ln 5 ln 2) ln2 2 2 2x x= + + = =
e)
1 1 22 1
5 02 20 0
( 4 5)2 1 1 1 1 2ln 4 5 (ln2 ln 5) ln
2 2 2 2 54 5 4 5
d x xxI dx x x
x x x x
+= = = + = =
+ +
a)
2
1 21
dxI
x
= b) 0
2 21(2 1)
dxI
x
=
c) 1
3 20(3 1)
dxI
x
=+
Bi gii
a)
2
21 12
1
1 1 11
2 2
dxI
xx
= = = + =
b)
0 0
02 12 2
1 1
(2 1)1 1 1 1 1 1.
2 2 2 1 2 6 3(2 1) (2 1)
d xdxI
xx x
= = = = =
c)
1 1
13 02 2
0 0
(3 1)1 1 1 1 1 1.
3 3 3 1 12 4 6(3 1) (3 1)
d xdxI
xx x
+= = = = + =
++ +
a)
1
31
0
xI e dx= b)
1
32
0
(2 1)x xI e e dx= + c) 1
33
0
(1 4 )x xI e e dx=
d)
1
4
01
x
x
e dxI
e
=+
e) 2 2
5 2 21( 1)
x
x
e dxI
e
=
f)2 2
6 2 31(1 3 )
x
x
e dxI
e
=
g)
1
7
0
2 1x xI e e dx= + h) 1
2 28
0
1 3x xI e e dx= + i) 1
9
0 1
x
x
e dxI
e
=+

GV. Lu Huy Thng 0968.393.899
a)
1 33 3 1
1 0
0
1 1
3 3 3
x x eI e dx e= = =
b)
1 1 43 3 1
2 0
0 0
(2 1)1 1(2 1) (2 1) (2 1) .
2 2 4
xx x x x e
I e e dx e d e+
= + = + + =
4(2 1)1 81
2 4 4
e + =
4(2 1) 81
8 8
e +=
c)
1 1
3 33
0 0
1(1 4 ) (1 4 ) (1 4 )
4
x x x xI e e dx e d e= =
4 4 410
(1 4 ) (1 4 ) 81 (1 4 )1 1 81.4 4 4 4 4 16
xe e e
= = =
d)
1 1
14 0
0 0
( 1) 1ln 1 ln( 1) ln2 ln
21 1
xxx
x x
d ee dx eI e e
e e
+ += = = + = + =
+ +
e)
2 2 22 22
5 12 2 2 2 2 4 2 41 1
( 1)1 1 1 1 1.
2 2( 1) ( 1) 1 2( 1) 2( 1) 2( 1)
xx
x x x
d ee dx eI
e e e e e e
= = = = + =
f)
2 2 222
6 12 3 2 3 2 2 4 21 1
(1 3 )1 1 1 1 1.
6 6(1 3 ) (1 3 ) 2(1 3 ) 12(1 3 ) 12(1 3 )
xx
x x x
d ee dxI
e e e e e
= = = =
g)
1 1
17 0
0 0
1 1 2 12 1 2 1 (2 1) . (2 1) 2 1 (2 1) 2 1 3
2 2 3 3
x x x x x xI e e dx e d e e e e e= + = + + = + + = + +
h)
1
2 28
0
1 3x xI e e dx= +1
2 2 2 2 1 2 20
0
1 1 2 1 81 3 (1 3 ) . (1 3 ) 1 3 (1 3 ) 1 3
6 6 3 9 9
x x x xe d e e e e e= + + = + + = + +
i)
1
9
0 1
x
x
e dxI
e
=+
1
10
0
( 1)2 1 2 1 2
1
xx
x
d ee e
e
+= = + = +
+
a) 11
lne
xI dx
x= b) 2
1
3 ln 1e
xI dx
x
+= c)
3
3
1
(3 ln 1)e
xI dx
x
+=
d) 3 2
4
1
4 ln 3 ln 2 ln 1e
x x xI dx
x
+ += e)
2
5 ln
e
e
dxI
x x= f) 6
1(3 ln 1)
e
dxI
x x=
+

GV. Lu Huy Thng 0968.393.899
B HC V B - CHUYN CN S N BN Pa

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