Question

How do you find the integral of `int cos^3(x) sin^4(x) dx`?

Answer 1

`(sin^5 x)/5 + (sin^7 x)/7 +C`

Explanation:

`intcos^3 xsin^4 xdx=intcosxcos^2 xsin^4 xdx=`
`intcosx(1-sin^2 x)sin^4 xdx=I`
`sinx=t => cosxdx=dt`
`I=int(1-t^2)t^4dt=t^5/5-t^7/7+C=`
`I=(sin^5 x)/5 + (sin^7 x)/7 +C`