If you don't want to use long-division, you can just do a trick...
etc...
The question
My attempt
Normally I'd use polynomial division to produce a rational integrand, but as you can see, the large power of u causes the division process to become quite lengthy. Is there a more efficient way of producing an easily solvable integrand?
Thanks.
An alternative:
Using the substitution we can obtain a closed solution:
Fernando Revilla
Edited: I forgot the binomial coefficients.
This is incorrect. is not equal to . You forgot the binomial coefficients. .
O ... ps !, of course. More than incorrect. I need a mathematical psychiatrist I see.
Fernando Revilla