How Do You Solve the Integral of sin^3(x)cos^6(x)dx?

[Saterial]

Homework Statement

∫sin^3xcos^63xdx

Homework Equations

The Attempt at a Solution

∫sin^3xcos^63xdxsin^3xcos^63xdx

let u=cosx
du=-sinxdx
-du=sinxdx

=∫sin^2xcos^63xsinxdx
=∫(1-cos^2x)cos^63x-du
=-∫(1-u^2)u^63du
=-∫(u^63-u^65)du
=-u^64/64-u^66/66+c
=(-cos^64x/64)-(cos^66x/66)+c

^ I'm thinking this is not the correct answer?

 

[vela]

Try differentiating it and see if you recover the integrand.