Question

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

Answer 1

`I = (6sin^7x)/7-(2sin^9x)/3+C`

Explanation:

`I = int (6sin^6x)(cos^3x)dx = 6int sin^6x cos^2x cosxdx`

`I = 6int sin^6x (1-sin^2x) cosxdx`

`sinx=t => cosxdx=dt`

`I = 6int t^6 (1-t^2) dt = 6 int (t^6-t^8)dt = 6 (t^7/7-t^9/9+C)`

`I = (6sin^7x)/7-(2sin^9x)/3+C`