What is the integral of sin ^3 x.

We have to determine the value of Int [ (sin x)^3
dx]

Int [ (sin x)^3
dx]

=> Int [ (sin x)^2* sin x
dx]

=> Int [ (1 – (cos x)^2 )* sin x
dx]

let u = cos x => du = -sin x
dx

=> Int [ (1 – u^2 )*
(-du)]

=> u^3/3 – u +
C

substitute u = cos
x

=> ( cos x)^3 / 3 – cos x +
C

The integral is (cos x)^3/ 3 – cos x +
C