   Chapter 8.5, Problem 29E ### 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. ∫ sec 6 x 4 tan   x 4 d x

To determine

To calculate: The integral of sec6x4tanx4dx.

Explanation

Given Information:

The provided integral is sec6x4tanx4dx.

Formula used:

Write the formula of integral of un.

undu=un+1n+1+C

Write the formula for derivative of secu.

ddx[secu]=secutanududx

Calculation:

Consider u=secx4.

Differentiate the above considered function.

du=secx4tanx4(14)dx=14secx4tanx4dx

The provided integral is,

sec6x4tanx4dx

Multiply and divide by 4.

sec6x4tanx4dx=4(secx4)5(14secx4tanx4dx)

Substitute u for secx4 and du for 14secx4tanx4dx

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