Question

решить интеграл cos3x sin^5 3x dx

Answer 1

$intlimits {cos(3x)sin^5(3x)} , dx = intlimits {cos(3x)sin^5(3x)* frac{1}{cos(3x)*3} } , dx =\= intlimits {sin^5(3x)*} frac{1}{3} , dx \sin(x)=t\intlimits { frac{t^5}{3} } , dt= frac{1}{3}intlimits {t^5} , dt = frac{1}{3}* frac{sin^6(3x)}{6}= frac{sin^6(3x)}{18} +C$
C∈R