Please help..

Question

ʃ (4sin²x cos²×/sin 2x cos 2x)dx

That's integration of (4sin^2x cos^2x over sin 2x cos 2x) dx

i've got it from the back and it has an answer from the back page of the book but i want to know how to solve it..i really need it for practicing this subject...please please help..Thanks a lot..
the answer is: -1/2 ln|secx + tanx| + c

Answer 1

4sin^2(x)cos^2(x)=(sin2x)^2
(sin2x/cos2x)dx=(-1/2)d(cos2x)/cos2x

Answer 2

Hmm. There's something wrong here. Mgraph's solution is correct, but is not what you were expecting.

ln|secx + tanx| is the integral of secx, not sinx/cosx

Is there a typo somewhere?