   Chapter 8.5, Problem 14E ### 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 2 x cot   x   d x

To determine

To calculate: The integral of csc2xcotxdx.

Explanation

Given Information:

The provided integral is csc2xcotxdx.

Formula used:

Write the formula of integral of 1udu.

1udu=ln|u|+C

Write the formula for derivate of cotu.

ddx[cotu]=csc2ududx

Calculation:

Consider u=cotx.

Differentiate the above considered function.

du=csc2xdx

The provided integral is,

csc2xcotxdx

Rewrite.

csc2xcotxdx=1cotx(csc2xdx)

Substitute u for cotx and du for csc2xdx

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