反正切arctanX的不定积分？？？我知道是用分部积分法求解，但求具体步骤，

Question

如题所述

Answer 1

∫arctanxdx
=xarctanx-∫xd(arctanx)
=xarctanx-∫xdx/(1+x²)
=xarctanx-1/2*∫d(x²+1)/(x²+1)

=xarctanx-1/2*ln(x²+1)+C本回答被提问者和网友采纳

Answer 2

∫arctanxdx＝xarctanx-∫xd(arctanx)＝xarctanx-∫x/(1+x^2)dx＝xarctanx-1/2ln(1+x^2)+C