   Chapter 8.5, Problem 12E ### 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   x   csc 2   x   d x

To determine

To calculate: The integral of cotxcsc2xdx.

Explanation

Given Information:

The provided integral is cotxcsc2xdx.

Formula used:

Write the formula of integral of un.

undu=un+1n+1+C

Write the formula for derivative of cotu.

ddx[cotu]=csc2ududx

Write the formula for derivative of xn.

ddxxn=nxn1

Calculation:

Consider u=cotx.

Differentiate the above considered function.

du=csc2xdx

The provided integral is,

cotxcsc2xdx

Rewrite.

cotxcsc2xdx=(cotx)1/2(csc2xdx)

Substitute u for cotx and du for csc2xdx

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