Question

Evaluate:

`int sin^3x cos^3x  dx`

Answer 1

I = `int sin^3x cos^3x  dx`

= `int sin^3x * cos^2x * cos x  dx`

= `int sin^3x (1 - sin^2x)cosx  dx`

Put sin x = t

`\implies` cos x dx = dt

∴ I = `int t^3(1 - t^2)dt`

= `int (t^3 - t^5)dt`

= `t^4/4 - t^6/6 + c`

= `(sin^4x)/4 - (sin^6x)/6 + c`