Question

. Evaluate ∫ cot 2x dx. A. 1⁄2 Ln csc 2x + C B. 1⁄2 Ln cos 2x + C C. 1⁄2 Ln sin 2x + C D. 1⁄2 Ln sec 2x + C

Answer 1

cot(2x)dx = [cos(2x) / sin(2x)] dx, and note that the derivative of sin(2x) = 2cos(2x)dx, which is double of the numerator.
Therefore, this can be integrated using an ln function of sin. This results in:
(1/2)ln(sin2x) + C
This is choice C.