Question

Integrate the following with respect to x.

sin³x

Answer 1

sin³x = 3 sin x – 4sin³x

4sin³x = 3 sin x – sin³x

⇒ sin³x = `1/4 [3 sin x - sin^3x]`

`int sin^3x  "d"x = 1/4  int (3 sin x - sin^3x)  "d"x`

= `1/4 [3(- cos x) - ((- cos 3x)/2)] + "c"`

= `(-3)/4 [cos x] + 1/12 [cos 3x] + "c"`