   Chapter 8.5, Problem 9E ### 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 9 x   tan 9 x   d x

To determine

To calculate: The integral of sec9xtan9xdx.

Explanation

Given Information:

The provided integral is sec9xtan9xdx.

Formula used:

Write the formula of integral of secutanu.

secutanudu=secu+C

Write the formula for derivative of xn.

ddxxn=nxn1

Calculation:

Consider u=9x.

Differentiate with respect to x,

d(u)dx=d(9x)dx=9

And,

du=9dx

The provided integral is,

sec9xtan9xdx

Multiply and divide by 9.

sec9xtan9xdx=19(sec9xtan9x)9dx

Substitute u for 9x and du for 9dx

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