Question

What is the integral of `(x^2)(lnx)`?

Answer 1

`int x^2*Lnx*dx=x^3/3*Lnx-x^3/9+C`

Explanation:

After setting `dv=x^2*dx` and `u=Lnx` for using integration by parts, `v=x^3/3` and `du=dx/x`

Hence,

`int udv=uv-int vdu`

`int x^2*Lnx*dx=x^3/3*Lnx-int x^3/3*dx/x`

=`x^3/3*Lnx-int x^2/3*dx`

=`x^3/3*Lnx-x^3/9+C`