Some problem occured in proving the following reduction formula.
$ \\ I_{(m,n)}\; =\;\int x^m(x+a)^ndx\; = \; \frac{x^m(x+a)^{n+1}}{m+n+1}-\frac{ma}{m+n+1}I_{(m-1,n)}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;m,n \in N $ I have tried by using integration by part,here are my result
$ \begin{align} I_{(m,n)}\; =\;\frac{x^{m+1}(x+a)^n}{m+1}-\frac{n}{m+1}I_{(m+1,n-1)}\\ I_{(m,n)}\; =\;\frac{x^{m}(x+a)^{n+1}}{n+1}-\frac{m}{n+1}I_{(m-1,n+1)} \end{align} $ I have no idea on how to combine the 2 result or my direction of attacking the problem is wrong. Any help would be appreciated.Thank you.