∫x/(1+√x)dx在0,1定积分
问题描述：
∫x/(1+√x)dx在0,1定积分
答
令t=√x,x=t²,t∈[0,1]
dx=2t
∫[0->1] √x/(1+x)dx=2∫[0->1] t²/(1+t²)dt
=2∫[0->1] 1-[1/(1+t²)]dt
=2-2arctant | [0->1]
=2-π/2