Question

求下列定积分

求积分

Answer 1

let
u=√x
2u du =dx
x=0, u=0
x=1, u=1
∫(0->1) dx/(1+√x)
=∫(0->1) 2u du/(1+u)
=2∫(0->1) [1 - 1/(1+u)] du
=2[ u -ln|1+u|]|(0->1)
=2( 1- ln2)
=2-2ln2