积分积不出来求∫(下限是0,上限是1)(1/(1+√x))dx,

Question

积分积不出来
求∫(下限是0,上限是1)(1/(1+√x))dx,

Answer 1

换元法：令√x=t
=∫2t/(1+t)dt
=2∫[1-1/(1+t)]dt
=2∫1dt-2∫1/(1+t)dt
=2-2ln2