Show given that
I don't see any way to get directly from one of these integrals to the other. So I think that you have to evaluate each integral separately and then compare them.
Let . Integrate by parts twice and you will find that if then
(using for the last step). Therefore , and so .
A similar calculation (integrating by parts twice) shows that . And a straightforward integration gives
Therefore and . The desired connection between and then follows.