Integrate [log(x-5) - log (x-3)] / [(x-5)(x-3)]?

Question

This is a Std XII Maharshtra board curriculum problem

Answer 1

To do this, let u = [log(x-5) - log (x-3)], the du = 1/(x-5) - 1/(x-3) = 2/(x-3)(x-5). So then you get the integral of udu/2 which is (1/4)u^2. Then when you plug back in for u, you get (1/4)[log(x-5) - log (x-3)]^2, which agrees with the previous poster and that Wolfram guy he cited.

Answer 2

1/4 [log (x-5) - log(x-3) ] ^2