## Calculus, 10th Edition (Anton)

Published by Wiley

# Chapter 4 - Integration - 4.2 The Indefinite Integral - Exercises Set 4.2 - Page 279: 24

#### Answer

$$x - \csc x + C$$

#### Work Step by Step

\eqalign{ & \int {\csc x\left( {\sin x + \cot x} \right)dx} \cr & {\text{multiply}} \cr & = \int {\left( {\csc x\sin x + \csc x\cot x} \right)dx} \cr & {\text{basic trigonometric identities}} \cr & = \int {\left( {\frac{1}{{\sin x}}\sin x + \csc x\cot x} \right)dx} \cr & = \int {\left( {1 + \csc x\cot x} \right)dx} \cr & = \int {dx} + \int {\csc x\cot x} dx \cr & {\text{find the antiderivative}} \cr & = x - \csc x + C \cr}

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