ʃ 1/(x^2+1)^2 dx

ʃ 1/(x^2+1)^2 dx
ʃ 1/(x^2+1)^2 dx

ʃ 1/(x^2+1)^2 dx
点击放大、再点击再放大:

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