The question is:

Prove (by mathematical induction) that:

I've proved the equality for n=1 as my base step. For my induction step I said that S(1) is true. Suppose that S(n)=S(k). We need to prove that S(k+1) is true. So the LHS becomes:

And I used integration by parts to get the expression

However I'm not sure what the RHS expression becomes for S(k+1). I thought it might be:

But I don't think that's correct. Any help appreciated! Many thanks.

CP