   Chapter 8.5, Problem 17E ### 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. ∫ sin x 1 + cos x d x

To determine

To calculate: The integral of sinx1+cosxdx.

Explanation

Given Information:

The provided integral is sinx1+cosxdx.

Formula used:

Write the formula of integral of 1udu.

1udu=ln|u|+C

Write the formula for derivate of cosu.

ddx[cosu]=sinududx

Calculation:

Consider u=1+cosx.

Differentiate the above considered function.

du=sinxdx

The provided integral is,

sinx1+cosxdx

Rewrite.

sinx1+cosxdx=11+cosx(sinxdx)

Substitute u for 1+cosx and du for sinxdx

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