Integrate sin9x cos3x dx ?

1 Answer
Apr 4, 2018

I=124(cos(12x)+2cos(6x))+C

Explanation:

We want to solve

I=sin(9x)cos(3x)dx

Use the product identity

sin(a)cos(b)=12(sin(a+b)+sin(ab))

Thus

I=12sin(9x+3x)+sin(9x3x)dx

I=12sin(12x)+sin(6x)dx

I=12(112cos(12x)16cos(6x))+C

I=124(cos(12x)+2cos(6x))+C