高等数学A上册习题解答 至微分中值定理(8)

华中师范大学专用

{1:(n {)x=tant

x2

(x2+1)2dx

tan2tsec2=t=

sec4tdt

sin2tdt= 12[1 cos2t]dt

=12[t 1

2

sin2t]=1

2arctanx

x2(x2+1)+C. {2:(©ÜÈ©{)

x2

=

(x2+1)2dx

x2d1x+1

= x1

12x+1 x+1d x2

=

x11

2x2+1+1

2x2+1dx=12arctanx x2(x+1)+C.8

(0.13)

(0.14)