   Chapter 8.5, Problem 8E ### 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. ∫ csc 2 4 x   d x

To determine

To calculate: The integral of csc24xdx.

Explanation

Given Information:

The provided integral is csc24xdx.

Formula used:

Write the formula of integral of csc2u.

csc2udu=cotu+C

Write the formula for derivative of xn.

ddxxn=nxn1

Calculation:

Consider u=4x.

Differentiate with respect to x,

d(u)dx=d(4x)dx=4

And,

du=4dx

The provided integral is,

csc24xdx

Multiply and divide by 4.

csc24xdx=14(csc24x)4dx

Substitute u for 4x and du for 4dx

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