Question

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

Answer 1

`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`