Find the integral `int sin^5x*cos^2x dx`

1 Answer | Add Yours

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The integral `int sin^5x*cos^2x dx` has to be determined.

 `int sin^5x*cos^2x dx`

=> `int sin x*(1 - cos^2x)^2*cos^2x dx`

let `cos x = y => dy = -sin x dx`

=> `-int (1 - y^2)^2*y^2 dy`

=> `-int (1 + y^4 - 2*y^2)*y^2 dy`

=> `-int y^2 + y^6 - 2*y^4 dy`

=> `-(y^3/3 + y^7/7 - 2y^5/5)`

=> `(2y^5)/5 - y^7/7 - y^3/3`

substitute y = cos x

=> `(2*cos^5x)/5 - (cos^7x)/7 - (cos^3x)/3`

The integral `int sin^5x*cos^2x dx = (2*cos^5x)/5 - (cos^7x)/7 - (cos^3x)/3`

We’ve answered 318,907 questions. We can answer yours, too.

Ask a question