Question

What is the integral of `xln(x)`?

Answer 1

You have to use the Integration by Parts formula: `intudv=uv-intvdu`

let u= lnx
du = `1/x`

dv = x
v = `x^2/2`

Plug this in the IBP formula and you'll get.

=`lnx*x^2/2 - intx^2/2*1/x`
Solve the integral on the right side and you'll get `-x^2/4`

Final answer would be: `lnx*x^2/2-x^2/4`