What is the integral of int sin^3 (x)cos^3 (x) dx?

1 Answer
Mar 7, 2016

int sin^3 x cos^3 x d x=1/4sin^4 x-1/5sin^5 x+C

Explanation:

int sin^3 x cos^3 x d x= ? " "sin x=u" "cos x d x=d u
int sin^3 x* cos^2 x* cos x* d x" "cos^2 x=1-sin^2 x
int u^3(1-sin^2)d u" "int u^3(1-u^2) d u" "int(u^3-u^5)d u
int sin^3 x cos^3 x d x=1/4u^4-1/5u^5+C
int sin^3 x cos^3 x d x=1/4sin^4 x-1/5sin^5 x+C