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Q. 54

Expert-verified

Calculus

Found in: Page 362

Book edition 1st

Author(s) Peter Kohn, Laura Taalman

Pages 1155 pages

ISBN 9781429241861

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Short Answer

Use integration formulas to solve each integral in Exercises 21–62. You may have to use algebra, educated guess- and- check, and/or recognize an integrand as the result of a product, quotient, or chain rule calculation. Check each of your answers by differentiating. (Hint for Exercise 54: $\tan (x) = \frac{\sin (x)}{\cos (x)}$ ).
$\int \tan x d x .$

The value of the given integral is $- \ln (\cos x) + c .$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information.

Given is a integral: $\int \tan x d x .$

Step 2. Formula involved.

$\int \frac{1}{t} d t = \ln t + c .$

Step 3. Solving the integral.

$\int \tan x d x = \int \frac{\sin x}{\cos x} d x L e t t = \cos x d t = - \sin x d x P u t t i n g t h e v a l u e i n t h e i n t e g r a l = \int - \frac{1}{t} d t = - \ln t + c = - \ln (\cos x) + c .$

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