Answer
$$\ln |\sin x|+c $$
Work Step by Step
We have
$$\int \cot x dx = \int \frac{\cos x}{\sin x}dx=\\
\ln |\sin x|+c $$
Where we used the facts that $(\sin u)'=\cos u $ and $\int \frac{u'}{u}=\ln u $.
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 7 - Exponential Functions - 7.3 Logarithms and Their Derivatives - Exercises - Page 343: 93
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