Question

How do you find the integral of `int sin^6(x) cos^3(x) dx`?

Answer 1

`int sin^mxcos^nx dx` with one (or both) `m, n` odd should be added to your mathematics recipe book.

Explanation:

Because sine and cosine are (up to a mminus sign) derivatives of each other, we can integrate by substitution.

Regroup one the the functions that has an odd exponent to join `dx`. This pair will be `du` when we make a substitution. It also leaves an even power that can be rewritten using `sin^2x+cos^2x =1`

Do the substitution, expand and integrate the resulting polynomial.

Reverse the substitution to finish.