Integrate: cos(3X)*sin^2 (3X)*dx?

Question

Integrate: cosine of 3x times sine squared of 3x times derivative of x.

The answer is 1/9 sine cubed, times 3X plus C
or
1/9 sin^3(3X)+C

Answer 1

cos(3x)*sin^2 (3x)*dx
Let u = sin(3x)
du = 3cos(3x)dx
then
cos(3x)*sin^2 (3x)*dx =
(1/3)u^2du
∫(1/3)u^2du =
(1/9)u^3 + C =
(1/9)sin^3(3x) + C
or
(1/9)(sin(3x))^3 + C