Prove the identity:

*Proof.* Using the hint (that ) we start with the expression on the left,

(The interchange of the sum and integral is fine since it is a finite sum. Those planning to take analysis should note that this cannot always be done in the case of infinite sums.) Now, we have a reasonable integral, but we still want to get everything back into the form of the sum on the right so we make the substitution , . This gives us new limits of integration from 1 to 0. Therefore, we have

*Related*