Question

What is the integral of `int xlnx dx`?

Answer 1

`= x^2/2 ln x - x^2/4 + C`

Explanation:

we use IBP

`int u v' = uv - int u' v`

`u = ln x, u' = 1/x`
`v' = x, v = x^2/2`

`= x^2/2 ln x - int dx qquad x/2`

`= x^2/2 ln x - x^2/4 + C`