微积分求解：∫√x/(1+x) dx

题目

微积分求解：∫√x/(1+x) dx

答案

设t=√x,t^2=x,dx=2tdt,则∫√x/(1+x)dx =∫2t^2/(1+t^2)dt
=2∫t^2/(1+t^2)dt =2(∫1-1/(1+t^2)dt) =2(t-arctant) +C
=2(√x-arctan√x) +C