Question

What is the integral of `ln(sqrt(x))`?

Answer 1

By part :

`intln(sqrt(x))dx`

`du = 1`
`u = x`

`v = ln(sqrt(x))`
`dv = 1/(2x)`

`[xln(sqrt(x))]-1/2intdx`

`[xln(sqrt(x))-1/2x]`

don't forget `ln(a^b) = bln(a)`

`[1/2xln(x)-1/2x]`

factorize by `1/2x` and don't forget the constant !

`[1/2x(ln(x)-1)+C]`