Question

How to integrate 2sin3xsin2x?

Answer 1

How would I integrate (2 sin3x sin 2x dx)?

Let I=∫2sin(3x)sin(2x)dx

As 2sin(3x)sin(2x)=cos(3x−2x)−cos(3x+2x)

=cos(x)−cos(5x)

So, I=∫cos(x)−cos(5x)dx

=sin(x)−sin(5x)5+C (where C is the arbitrary constant of indefinite integration)