Question

How do you integrate `int x^2lnx` by parts from `[1,2]`?

Answer 1

`int_1^2x^2lnxdx=8/3ln2-7/9`

Explanation:

`int_1^2x^2lnxdx=int_1^2lnx d(x^3/3) = [x^3/3lnx]_1^2 - int_1^2x^3/3d(lnx) = 8/3ln2-int_1^2x^3/3(dx)/x=8/3ln2-int_1^2x^2/3dx=8/3ln2-[x^3/9]_1^2=8/3ln2-7/9`