   Chapter 8.5, Problem 21E ### 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   3 x   d x

To determine

To calculate: The integral of csc3xdx.

Explanation

Given Information:

The provided integral is csc3xdx.

Formula used:

Write the formula of integral of cscu.

cscudu=ln|cscu+cotu|+C

Write the formula for derivative of un.

ddxun=nun1

Calculation:

Consider u=3x.

Differentiate the above considered function.

du=3dx

The provided integral is,

csc3xdx

Multiply and divide by 3.

csc3xdx=13csc3xdx

Substitute u for 3x and du for 3dx

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