Given an integral of a function parametrized with respect to an integer index n, prove a given recursive identity and use this to evaluate the integral for a specific value of n.

This exercise is interesting as it combines a variety of concepts fundamental to integration and maths in general. It also allows to introduce the student to the idea of recursion, very often used to solve mathematical and computational problems.Integration by parts will be used to solve the integral and to prove the recursive relation. Finally Such relation will be exploited to find the third element of the series. Solution will be provided on the whiteboard.