How do you find the antiderivative of sin^3(x) cos^2(x) dxsin3(x)cos2(x)dx?

1 Answer
May 3, 2018

= - 1/3 cos^3 x + 1/5cos^5 x + C=13cos3x+15cos5x+C

Explanation:

int \ sin^3 x \ cos^2 x \ dx

int \ sin x( 1- cos^2 x) \ cos^2 x \ dx

= int \ sin x \ cos^2 x - sin x cos^4 x \ dx

= int \ ( - 1/3 cos^3 x)^' - ( -1/5cos^5 x)^' \ dx

= - 1/3 cos^3 x + 1/5cos^5 x + C