Question

What is the integral of `int sin^3(x)cos^4(x) dx`?

Answer 1

`int sin^3(x)cos^4(x) dx = -1/5cos^5(x)+1/7cos^7(x) + C`

Explanation:

`int sin^3(x)cos^4(x) dx`

but

`sin^3(x)cos^4(x) =(1-cos^2(x))cos^4(x) sin(x)`
`=cos^4(x) sin(x)-cos^6(x) sin(x)`

then

`int sin^3(x)cos^4(x) dx = int(cos^4(x) sin(x)-cos^6(x) sin(x))dx`
`=-1/5cos^5(x)+1/7cos^7(x) + C`