great question. not sure how valid my solution is. i did IBP once, then said pattern follows such that...^n dx = \frac{m!n!}{(m+n+1)!})
How did you get that?great question. not sure how valid my solution is. i did IBP once, then said pattern follows such that...
!}\int_{0}^{1}x^{n+m}dx )
one application of IBP with dv/dx = x^m & u = (1-x)^n gave a solutions of (n/m)(same integral but m is now m+1, n is now n-1). By repeating the process n times, you get what i've got in my last post.
Just thought of thisThere's an even more elegant substitution that kills the integral in 1 go. This was in my 3rd assessment task for school and yeah my method was the exact same as yours.
