Một số bài tập tích phân khá hay

Tính các tích phân sau:
a)
2
4
0
sin 2x
I dx
1 cos x
π
=
+
∫
; b)
2
2
2
3
1
I dx
x x 1
=
−
∫
; c)
2
2
1
ln(x 1)
I dx
x
+

=
∫
;
d)
2 3
2
0
sin x
I dx
1 cos x
π
=
+
∫
e)
2
2
2
x cosx
I dx
4 sin x
π
π
−
+
=
−
∫
4
3

0
x sin x
I dx
cos x
π
=
∫
2
3
0
I x.cos x.sinx.dx
π
=
∫
3
3 2
1
1
I dx
x x 1
=
+
∫
2
0
4 x
I (x 2) dx
4 x
−
= −

+
∫
2
2
1
1
I dx
x 1 ln x
=
−
∫
ln3
2x
x
0
e
I dx
1 e
=
+
∫
2
3
1
1
I dx
x(x 1)
=
+
∫

0
x
I dx
1 sin x
π
=
+
∫
0
2
1
1
I dx
2x 4x 2
−
=
− − +
∫
2
2
0
sin 2x
I dx
(2 sin x)
π
=
+
∫
4
0

x
I dx
1 2x 1
=
+ +
∫
2 3
0
4sin x
I dx
1 cosx
π
=
+
∫
1
1
2
1 x dx
I
1 x x
−
−
=
+
∫
8
0
2sin 2x 3sin x
I dx

6cos x 2
π
+
=
−
∫
2
0
sin x cos x
I dx
sin x 2cos x
π
−
=
+
∫
e
1
3 2ln x
I dx
x 1 2ln x
−
=
+
∫
4
0
x
I dx
1 cos 2x

π
=
+
∫
7
3
0
x 2
I dx
x 1
+
=
+
∫
1
2
2
0
x 1
I dx
4 x
+
=
−
∫
2
2
0
2sin x.cos x
I dx

13 5cos x
π
=
−
∫
2 3
2
0
cos x.sin x
I dx
1 sin x
π
=
+
∫
3
2
4
tan x
I dx
cosx 1 cos x
π
π
=
+
∫
1
2
1
3

2
I dx
x 4x 1
=
−
∫
2
0
I ( sin x cos x )dx
π
= −
∫
6
6 6
x
6
sin x cos x
I dx
2009 1
π
−π
+
=
+
∫
6
3
0
tan x
I dx

cos2x
π
=
∫