Use table of integrals to evaluate the integral of x^4 sinxdx.
so, find a table of integrals and look it up. You will probably just find some power reduction formulas, such as
∫ x^n sinx dx = -x^n cosx + n∫ x^(n-1) cosx dx
You can see that you will have to use integration by parts 4 times to get rid of all the x^n terms.
So, you start out with
∫x^4 sinx = -x^4 cosx + 4∫x^3 cosx dx
and plug away from there