How do you find the integral of [x4(sinx)dx]?

1 Answer
Jun 13, 2018

x4sinxdx=(4x324x)sinx(x412x2+24)cosx+C

Explanation:

You need to integrate by parts repeatedly, to reduce the degree of x:

x4sinxdx=x4ddx(cosx)dx

x4sinxdx=x4cosx+4x3cosxdx

x4sinxdx=x4cosx+4x3ddx(sinx)dx

x4sinxdx=x4cosx+4x3sinx12x2sinxdx

x4sinxdx=x4cosx+4x3sinx+12x2cosx24xcosxdx

x4sinxdx=x4cosx+4x3sinx+12x2cosx24xsinx+24sinxdx

x4sinxdx=x4cosx+4x3sinx+12x2cosx24xsinx24cosx+C