Question

How do you find the integral of `(sinx)^3 dx`?

Answer 1

Refer to explanation

Explanation:

We know that

#sin 3x = 3sinx - 4 (sin x)^3=>4(sinx)^3=3sinx-sin3x=> (sinx)^3=3/4*sinx-1/4sin3x #

Hence we have that

`int (sinx)^3 dx=int (3/4*sinx-1/4*sin(3x))dx=-3/4cosx+1/12cos3x+c`