arctan（x）^1/2的不定积分

题目

arctan（x）^1/2的不定积分

答案

√x=u,dx=2udu
=∫2arctanudu^2
=2u^2arctanu-2∫u^2/(1+u^2)*du
=2u^2arctanu-2∫(u^2+1-1)/(1+u^2)*du
=2u^2arctanu-2u+2arctanu+C
=2xarctan√x-2√x+2arctan√x+C