   Chapter 8.5, Problem 24E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Integrating a Trigonometric Function In Exercises 1–32, find the indefinite integral. See Examples 1, 2, 3, 4, 5, and 8. ∫ e − x tan   e − x d x

To determine

To calculate: The integral of extanexdx.

Explanation

Given Information:

The provided integral is extanexdx.

Formula used:

Write the formula of integral of tanu.

tanudu=ln|cosu|+C

Write the formula for derivative of eu.

ddx[eu]=eududx

Calculation:

Consider u=ex.

Differentiate the above considered function.

du=exdx

The provided integral is,

extanexdx

Rewrite the expression as:

extanexdx=(tanex)(exdx)

Substitute u for ex and du for exdx

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