@vv 

Okay, I understand.

A follow-up question. I have come across a few table of integrations with hypergeometric http://functions.wolfram.com/HypergeometricFunctions/Hypergeometric2F1/21/ShowAll.html

Is it common knowledge that one has to check the sum in the function for been divergent or not? Before using the table?

@vv

First of all thanks! I get the idea and understand the problem of a divergent integral.

But if you have time could you explain the steps in between?

1. function op: You simply replace F, not sure why, but okay. And the sum is removed. I guess you simply switch the sum and integral.

2. The function is divided by iteself, but i is increased with one in the numerator. What is this?