不定积分ln(x+1)/根号x dx
问题描述：
不定积分ln(x+1)/根号x dx
答
用分步积分法∫ln(x+1)/√x dx=2∫ln(x+1)d√x =2ln(x+1)*√x -2∫√x dln(x+1)=2ln(x+1)*√x -2∫√x /(x+1)dx对于∫√x /(x+1)dx令√x=t,x=t^2,dx=2tdt∫√x /(x+1)dx=∫t/(t^2+1)*2tdt=2∫[1-1/(t^2+1)dt=2t-2arc...