Question

数学积分，简单一道题求解

ʃ 1/(x^2+1)^2 dx

Answer 1

点击放大、再点击再放大:

Answer 2

上下除以x^2有

x = tant dx =(sect)^2 dt

原式变为 ( 1/(sect)^4 ) (sect)^2 dt
=(cost)^2 dt
=((cos2t + 1)/2) dt
=sin2t/4 + t/2 + C

再将t= arc tanx代入，得到答案