   Chapter 8.5, Problem 19E ### 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. ∫ cot   π x   d x

To determine

To calculate: The integral of cotπxdx.

Explanation

Given Information:

The provided integral is cotπxdx.

Formula used:

Write the formula of integral of cotu.

cotudu=ln|sinu|+C

Write the formula for derivative of un.

ddxun=nun1

Calculation:

Consider u=πx.

Differentiate the above considered function.

du=πdx

The provided integral is,

cotπxdx

Multiply and divide by π.

cotπxdx=1π(cotπx)πdx

Substitute u for πx and du for πdx

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