Question

Evaluate:

`int sin^3x cos^4x  dx`

Answer 1

Let `I = int sin^3x cos^4x  dx`

= `int sin^2x. cos^4x (sin x  dx)`

= `int (1 - cos^2x) cos^4x (sin x  dx)`

Let cos x = t

⇒ – sin x dx = dt

or sin x dx = – dt

∴ `I = int (1 - t^2) t^4 (- dt)`

= `-int (t^4 - t^6) dt`

= `int (t^6 - t^4) dt`

= `t^7/7 - t^5/5 + c`

= `cos^7x/7 - cos^5x/5 + c`