常用积分公式
（一）含有axb的积分a0
1．

dxax
b
＝
1a
l

ax

b

C
2．axbdx＝1axb1C（1）
a1
3．
xdx＝1axbbl
axbCaxba2
4．
x2ax
dxb
＝
1a3

12
ax

b2

2bax

b

b2
l

ax

b


C
5．
dxxaxb
＝1l
b
axbx
C
6．
dx＝1x2axbbx

ab2
l

axbx
C
7．
ax
x
b2dx
＝
1a2
l

ax

b

bax
b

C
8．
x2axb2dx
＝
1a3
ax

b

2bl

ax

b

b2ax
b

C
9．
dxxaxb2
＝1baxb

1b2
l

axbx
C
（二）含有axb的积分
10．axbdx＝2axb3C
3a
11．
x
ax

bdx
＝
215a2
3ax

2b
axb3C
12．
x2
ax

bdx
＝
2105a3
15a2
x2

12abx

8b2

axb3C
13．
xax
b
dx
＝
23a2
ax

2b
axbC
14．
x2dx＝23a2x24abx8b2axbC
axb15a3
1
f15．x

1
l

axbbC
dxax
b
＝



baxbb
2arcta
axbC
b
b
b0b0
16．
dx＝axba
dx
x2axb
bx2bxaxb
17．
axbdx＝2x
axbbx
dxaxb
18．
axx

2
b
dx
＝

axbax2
dxxaxb
（三）含有x2a2的积分
19．
dxx2a2

1a
arcta

xa
C
20．
x2
dxa2


2

x1a2x2

a2
1

2
32
1a2
dxx2a2
1
21．
dxx2a2
1l
2a
xaxa
C
（四）含有ax2ba0的积分
22．
1
dxax2
b
＝
2
arcta
ab1l
ab
axCbaxbaxb
C
b0b0
23．
xax2
dxb
＝
12a
l

ax2

b

C
24．
x2ax2
dxb
＝
xa

ba
dxax2b
25．
dx＝xax2b
1l
2b
x2ax2b
C
26．
dxx2ax2

b
＝

1bx

ab
dxax2b
2
f27．
dxx3ax2b
＝a2b2
l

ax2bx2

12bx2
C
28．
dxax2
b2
＝
x2bax2

b

12b
dxax2b
（五）含有ax2bxca0的积分


29．
ax2
dxbx

c
＝

2arcta
2axbC
4acb2
4acb2
1l
2axbb24acC
b24ac2axbb24ac
b24acb24ac
30．
ax2
xbx

dxc
＝
12a
l

ax2

bx

c

b2a
dxax2bxc
（六）含有x2a2a0的积分
31．
dxx2a2
＝arshxa
C1＝l
x
x2a2C
32．
dx
＝
x
C
x2a23a2x2a2
33．
xdx＝x2a2Cx2a2
34．
xdx＝1C
x2a23
x2a2
35．
x2dx＝xx2a2a2l
xx2a2C
x2a2
2
2
36．
x2
dx＝xl
xx2a2C
x2a23
x2a2
37．
dx＝1l
x2a2aC
xx2a2a
x
38．
x2
dx＝x2a2
x2a2a2x
C
39．x2a2dx＝xx2a2a2l
xx2a2C
2
2
3
f40．x2a23dx＝x2x25a2x2a23a4l
x
8
8
41．xx2a2dx＝1x2a23C
3
x2a2C
42．x2x2a2dx＝x2x2a2x2a2a4l
xx2a2C
8
8
43．x2a2dx＝x2a2al
x2a2aC
x
x
44．
x
2x2
a
2
dx
＝

x2a2l
xx
x2a2C
（七r