   Chapter 8.5, Problem 27E ### 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. ∫ e sin   π x cos   π x   d x

To determine

To calculate: The integral of esinπxcosπxdx.

Explanation

Given Information:

The provided integral is esinπxcosπxdx.

Formula used:

Write the formula of integral of du.

du=u+C

Write the formula for derivative of eu and, sinu.

ddx[eu]=eududx

And,

ddx[sinu]=cosududx

Calculation:

Consider u=esinπx.

Differentiate the above considered function.

du=esinπxcosπxπdx=πesinπxcosπxdx

The provided integral is,

esinπxcosπxdx

Multiply and divide by π

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