$j_n=\int_0^1 x^{2n}\sin(\pi x)dx$.
How do I show that $j_{n+1}= \frac{1}{\pi^2}\left[\pi-(2n+1)(2n+2)j_n\right]$?
I keep getting a recurring integration by parts and I can't simplify it.
Please show your working for me to see where I'm going wrong.
Many Thanks.