   Chapter 8.5, Problem 28E ### 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 sec   4 x sec   4 x   tan   4 x   d x

To determine

To calculate: The integral of esec4xsec4xtan4xdx.

Explanation

Given Information:

The provided integral is esec4xsec4xtan4xdx.

Formula used:

Write the formula of integral of du.

du=u+C

Write the formula for derivative of eu and, secu.

ddx[eu]=eududx

And,

ddx[secu]=secutanududx

Calculation:

Consider u=esec4x.

Differentiate the above considered function.

du=esec4x(sec4xtan4x)4dx=4esec4xsec4xtan4xdx

The provided integral is,

esec4xsec4xtan4xdx

Multiply and divide by 4

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