对反正切函数arctgx求不定积分应该用 ( )

1个回答

用分部积分法,选 D.
∫arctanxdx=∫xd(arctanx)
=x*arctanx-∫xdx/(1+x^2)
=x*arctanx-(1/2)∫d(1+x^2)/(1+x^2)
=x*arctanx-(1/2)ln(1+x^2)+C.