Find Int [cos 2x / (sin 2x)^3 dx]

Let F(x) = intg (cos2x / sin2x)^3
dx.

Let us assume that y =
sin2x.

==> dy = 2cos2x. dx ==> dx =
dy/2cos2x

Let us
substitute.

F(x) = int   cos2x/ y^3 *
dy/2cos2x

       = intg dy / 2y^3
.

       = intg (1/2) y^-3
dy

Let us
integrate.

==> F(x) = (1/2) y^-2 / -2  +
C

==> F(x) = (1/-4) y^-2 +
c

              = 1/(-4y^2)  +
C

Now we will substitute with y=
sin2x

==> F(x) =- 1/[4(sin2x)^2]  +
C