Question

How do you integrate `int x^2lnx` by integration by parts method?

Answer 1

Use integration by parts. Let `u = lnx` and `dv = x^2dx` Then `du = 1/xdx` and `v = 1/3x^3`.

`intx^2lnx dx= 1/3x^3lnx - int(1/3x^3 * 1/x)dx`

`intx^2lnxdx = 1/3x^3lnx - int1/3x^2dx`

`intx^2lnx dx= 1/3x^3lnx - 1/9x^3 + C`

Hopefully this helps!