(9)
dh2gh
(g是常数);
解
dhgh
h 2g
1
1
2dh
12g
1 2h2
C
2h
C. g
(10) (x 2)2dx;
1
解 (x 2)2dx (x2 4x 4)dx x2dx 4 xdx 4 dx x3 2x2 4x C.
3 (11) (x2 1)2dx;
12
解 (x2 1)2dx (x4 2x2 1)dx x4dx 2 x2dx dx x5 x3 x C.
53
x(1 x)2
x
le
(x
1
21 2x2
(13)
(1 x)2
dx;
ar
3 x2
1
)dx 2x2
122
x3 x2 x2 x C.
335
35
n.
3
5
解 (x 1)(x 1)dx (x x x 1)dx xdx
3232
3x4 3x2 1
(14) dx; 2
x 13x4 3x2 1123
解 dx (3x )dx x arctanx C. x2 1x2 1
x2
(15) dx;
1 x2x2x2 1 11
解 dx dx (1 )dx x arctanx C. 222
1 x1 x1 x
3
(16) (2ex dx;
x31
解 (2ex dx 2 exdx 3 dx 2ex 3ln|x| C.
xx
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解
dx
1 2x x2
x
ne
1
x2dx
(12) (x 1)(x3 1)dx;
42
x2 x2 C. 35
t
3
x2dx
dx