   Chapter 8.5, Problem 15E ### 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 x tan x sec   x − 1   d x

To determine

To calculate: The integral of secxtanxsecx1dx.

Explanation

Given Information:

The provided integral is secxtanxsecx1dx.

Formula used:

Write the formula of integral of 1udu.

1udu=ln|u|+C

Write the formula for derivate of secu.

ddx[secu]=secutanududx

Calculation:

Consider u=secx1.

Differentiate the above considered function.

du=secxtanxdx

The provided integral is,

secxtanxsecx1dx

Rewrite.

secxtanxsecx1dx=1secx1(secxtanxdx)

Substitute u for secx1 and du for secxtanxdx

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