Question

Find the intregration of sinx*cos2x*cos3x

Answer 1

That looks really promising, since the integrand is a polynomial in sin(x) all multiplied through by cos(x) . How convenient… let u=sin(x) so dx=sec(x)du and the integral becomes

I=∫u(1−2u2)(1−4u2)du=∫u−6u3+8u5du=u22−3u42+4u63+C=3sin2(x)−9sin4(x)+8sin6(x)6+