Calculus

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

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  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?

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