Calculus II Integration by parts

Question

Evaluate the integral: ∫6ln(x²-1)dx

Answer 1

I am not sure how to integrate this function by parts.

I would integrate it as follows:

ln(x²-1) = ln(x+1) + ln(x-1)

which integrates to (x+1)ln(x+1)-(x+1) + (x-1)ln(x-1) - (x-1) which you can collect (although it doesn't simplify it much!)

And don't forget the factor of 6.