Question

Integrate x2n-1 sin xn dx.

Answer 1

Integration:

$I= \int\limits^a_b {x^{2n-1}Sin\ x^n} \, dx = \int\limits^a_b {(x^n)*(x^{n-1}Sin\ x^n)} \, dx \\\\=x^n(-\frac{Cos\ x^n}{n})- \int\limits^a_b {(nx^{n-1})(-\frac{Cos\ x^n}{n})} \, dx \\\\=-\frac{1}{n}x^nCosx^n+\frac{1}{n}Sinx^n+K$