Answer
$-\frac {cos3x} 3 + \frac{cos^33x} 9+C$
Work Step by Step
$\int (sin3x)(sin^23x)dx$
$\int (sin3x)(1-cos^23x)dx$
$\int (sin3x-cos^23xsin3x)dx$
$\frac 1 3 \int sin3x(3)dx +\frac 1 3 \int cos^23x(-sin3x)(3)dx$
$\frac 1 3 (-cos3x)+\frac 1 3 (\frac {cos^33x} 3)+C$
$-\frac {cos3x} 3 + \frac{cos^33x} 9+C$
