What is the antiderivative of sin^3(2x)cos(2x)dx

Question

How would I solve the following: ∫sin³(2x)cos(2x)dx

Thank you so much!

Answer 1

If dF(x)/dx=f(x) F(x) is an anti-derivative of f(x).

d[(1/8)sin⁴(2x)]/dx = sin³(2x)cos(2x)

You can get this using u-substitution with u=sin(2x).