Question

用部分积分法求下列不定积分:∫arctan（√x）dx ,

Answer 1

简单计算一下即可，详情如图所示

Answer 2

∫arctan√x dx
令√x=t,x=t^2,dx=dt^2
所以
原式=∫arctantdt^2
=t^2*arctant-∫t^2/(1+t^2)dt
=t^2*arctant-∫(t^2+1-1)/(1+t^2)dt
=t^2*arctant-t+arctant+c
=xarctan√x-√x+arctan√x+c