Question

How do you integrate `int x^nsinx^(n-1)dx` using integration by parts?

Answer 1

I don't think you do. Here is the answer for `n=6` http://www.wolframalpha.com/input/?i=int+x%5E6sin%28x%5E5%29+dx

Explanation:

If you are not looking for an answer, you could, I suppose, use `u=x^2` and `dv=x^(n-2)sin(x^(n-1))dx` to get

`-1/(n-1)x^2cos(x^(n-1))-2/(n-1) int xcos(x^(n-1))dx`