1c2xl
2x1cdt∫11t1t3x1t∴xt213
（16）∫x3x1dx设
22222原式∫t2t21dtt5t3c3x153x13c945274527
（17）∫原式∫18
原式∫
dxxx1
2
设xsect∴tarccos
1x
111dsect∫dt∫darccosarccoscsectta
txx
∫
1x2dxx
设
xta
t
则
tarcta
x
1x2sect1ta
t1tdx∫dta
t∫dta
t∫dtsectl
ta
cxta
tsi
tsi
tsi
t21x21cxx
1x2l

19
∫
32xx2dx∫4x12dx
x1x14x12arcsi
c22
20
1
∫
xe
1x2
1
1x23
dx∫e
1x2
d
11x2
1
e
1x2
c
21
∫x
2
1111111l
xdx∫l
xdx3l
xx3∫x3dl
xx3l
x∫x2dxx3l
xx3c3333339
22
∫arcta

xdxxarcta
x∫xdarcta
xxarcta
x∫
x11dxxarcta
x∫1dx1x2x1x
xarcta
xxarcta
xc
f23
x1ex111xxx∫x22dx∫x1edx2x1ex2∫x2dx1e11exxxxx1eedxx1eeccx2∫x2x2
x
24
∫2x
2
12112111x2dx∫dxl
x2l
2x1l
c52x22x152252x13x2
25
∫x1
所以得
2
1dxx21
令
1ABCxD222x1x1x1x1x1
2
BC0AB2CD011ABCD0BC2D022ABD01x1111x2dx12∫x12dx2∫x1dx2∫x21dx2x111x11cl
c2x22x21
11于是原式∫222x1x11111l
x1l
x22x124
26
5x212x135x22x32x22x2dx∫dx∫52dx2∫x22x3x2x3x2x31∫5dx∫2dx22x3）5xl
x22x3cx2x3
27
x5x5x3811dx∫dx∫dx∫dx∫dx32422222x346x13x34x34x341x38∫dx3l
x26x134arcta
c22x34
∫x
2
28
f1x7ABx6C1x7dx令∫x1x7x1x7x1x7AB112x62则c0A1B2C0∴原式∫dxl
xl
1x7c7x1x7A1xl
c21x77
29
si
22x1cos2x11dx∫si
22xdx∫si
22xcos2xdx428811x11∫1cos4xdx∫si
22xdsi
2xsi
4xsi
32xc1616166448
24222∫si
xcosxdx∫si
xcosxcosxdx∫
（30）
si
r