\(\displaystyle \L \int\)sin3x⋅cos2xdx
\(\displaystyle \L\int\)sin2x⋅sinx⋅cos2xdx
\(\displaystyle \L\int\)(1−cos2x)(sinx)]⋅21(1+cos2x)dx
. . . . . . . . . . . . . . . . . . . No!
Don't introduce 2x into the problem
. . unless you can change everything to 2x
The answer is: 51cos5x−31cos3x+C