Question

How do you integrate `int x^4lnx` by integration by parts method?

Answer 1

`int x^n lnx dx = 1/(n+1)(x^(n+1)lnx-x^(n+1)/(n+1))+C`

Explanation:

`d/(dx)(x^n lnx) = n x^(n-1)lnx+x^(n-1)` or

`(n+1)int x^n lnx dx = x^(n+1)lnx-int x^n dx`

so

`int x^n lnx dx = 1/(n+1)(x^(n+1)lnx-x^(n+1)/(n+1))+C`