Các bài tập về nguyên hàm1.
Trang 1Các bài tập về nguyên hàm
1 ∫x dx5 2 17 dx
x
2x dx
(2x−3) dx
∫
6 1
1−x dx
7
x
x dx
5 x
dx
−
∫
1
x
dx
x
+
∫ 12 ∫x(1+x2 10) dx 13 2
1
dx
2
dx
∫ 15 ∫x(1−x dx)20
16 3
1 3
x
x dx
−
4 +1
1
dx
2
x dx
−
− +
x
dx
+
∫
21.∫cos 2xdx 22.∫sin 4xdx 23 cos(3 )
5
x−π dx
cos (3 1)
dx
dx
x−
2cos 1
xdx
x+
∫
26 sin( )
2 7
x
dx
π
+
sin 2
dx x
1 sin 2
dx x
+
1 sin 2
dx x
−
cos sin
dx
sin
dx
x
cos
dx x
cos sin
x dx
∫ 34 cos3 sin∫ x xdx 35 sin 4 sin∫ x xdx 36 2
tan
41 sin3
cos
x
dx
x
sin
2 cos3 sinx xdx
sin cos
dx
− +
sin cos 2
−
∫ x x x x dx
46.∫ (x a x b+ dx) ( + ) 47.∫xe 1 x− 2dx 48 ∫x x(3 +1)9dx 49 3 1
1
x x
e dx e
+ +
2 +1
51
dx
x
∫ 52.∫2 (4x x−1)5dx
sin cos 2 cos
4
=
54
2 4
2 2
1
55
2 4
2 2
1
56 (x 1)dx2 xdx2 dx2 ,
5
57
2
1 dx
,
dx
đặt t = cotx dt=
sin
sin 9cos
dx
∫
1 4
3
+
x
4 4
Trang 261.∫ (cos10x+sin10x dx)
62.∫ (cos8x+sin8x dx)
4 4
8 8
x
64 3
xdx
∫
2
2
1
+
∫
66 ( 1) ( 2) ( 3)
xdx
∫
67
4
1
dx x
−
∫
68 ∫x(1 x)− 2008.dx=∫ (x 1 1 (x 1)− + ) − 2008.dx=∫(x 1)− 2008dx+∫ (x 1 (x 1)− ) − 2008.dx
69 ( 4 3 2) ( )97 2 ( ) (2 )97 2 ( )99 ( 2 ) ( )99
x −2x +x 1 x− dx= x x 1 1 x− − dx= x 1 x− dx= − x − +1 1 x 1− dx
x 1 x 1 dx x 1 dx x 1 2 x 1 dx x 1 dx
x 1 dx 2 x 1 dx x 1 dx
1 2
71 cot4 12 1 cot 2
sin
x