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

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
If you are not looking for an answer, you could, I suppose, use $u = {x}^{2}$ and $\mathrm{dv} = {x}^{n - 2} \sin \left({x}^{n - 1}\right) \mathrm{dx}$ to get
$- \frac{1}{n - 1} {x}^{2} \cos \left({x}^{n - 1}\right) - \frac{2}{n - 1} \int x \cos \left({x}^{n - 1}\right) \mathrm{dx}$