习题4 1
1. 求下列不定积分:
1
(1) 2dx;
x111
解 2dx x 2dx x 2 1 C C.
2 1xx (2) xxdx; 解 xxdx
1x
3
x2dx
13 12
3 12x2 C
5
x2x C.
(3) 解
dx;
(4) x2xdx;
解 x2xdx
1
(5) 解
(6) xndx; 解
(7) 5x3dx;
5
解 5x3dx 5 x3dx x4 C.
4
(8) (x2 3x 2)dx;
13
解 (x2 3x 2)dx x2dx 3 xdx 2 dx x3 x2 2x C.
32
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x
7
x3dx
1
dx x
1
2dx
11
x2 C 2x C. 1 12
1
1
7 13
7 1
x3 C
33xx C. 10
x2x1
dx;
x2
x
dx x
5
2dx
1311
x2 C C. 52xx 12
5
xdx
n
n
xmdx
1
n 1m
n1
xm C
m
xn m
m nm
C.