Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - 6.2 Derivatives And Integrals Involving Logarithmic Functions - Exercises Set 6.2 - Page 426: 66

Answer

$$\ln \left| {\sin x} \right| + C$$

Work Step by Step

$$\eqalign{ & \int {\cot x} dx \cr & {\text{Using the trigonometric identity }}\cot x = \frac{{\cos x}}{{\sin x}} \cr & \int {\cot x} dx = \int {\frac{{\cos x}}{{\sin x}}} dx \cr & {\text{Set }}u = \sin x \to du = \cos xdx \cr & \int {\frac{{\cos x}}{{\sin x}}} dx = \int {\frac{{du}}{u}} \cr & {\text{integrate}} \cr & = \ln \left| u \right| + C \cr & {\text{substituting }}u = \sin x \cr & = \ln \left| {\sin x} \right| + C \cr} $$
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