Question

Evaluate (integral) cot 2x dx.

A. 1/2Ln sin 2x+C
B. 1/2Ln cos 2x+C
C. 1/2Ln sec 2x+C
D. 1/2LN csc 2x+C

Answer 1

First make the substitution
p=2x,
dp=2dx
dx=(1/2)dp
I=∫cot 2x dx
=∫cot(p)(1/2)dp
=(1/2)∫(cos(p)/sin(p))dp
=(1/2)∫d(sin(p))/sin(p)
=(1/2)ln sin(p) + C
Can you take it from here?