Question

How do you integrate `int x^3ln(5x)` by integration by parts method?

Answer 1

`int x^3ln(5x)dx = x^4/4(ln(5x)-1/4)`

Explanation:

`int x^3ln(5x)dx = int ln(5x) d(x^4/4) = x^4/4ln(5x) - int x^4/4 d(ln(5x)) = x^4/4ln(5x) - int x^4/4 1/xdx = x^4/4ln(5x)-int x^3/4dx=x^4/4ln(5x)- x^4/16dx=x^4/4(ln(5x)-1/4)`