   Chapter 8.5, Problem 30E ### 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 3 5 x   cot   5 x   d x

To determine

To calculate: The integral of csc35xcot5xdx.

Explanation

Given Information:

The provided integral is csc35xcot5xdx.

Formula used:

Write the formula of integral of un.

undu=un+1n+1+C

Write the formula for derivative of cscu.

ddx[cscu]=cscucotududx

Calculation:

Consider u=csc5x.

Differentiate the above considered function.

du=csc5xcot5x5dx=5csc5xcot5xdx

The provided integral is,

csc35xcot5xdx

Multiply and divide by 5.

csc35xcot5xdx=15(csc5x)2(5csc5xcot5xdx)

Substitute u for csc5x and du for 5csc5xcot5xdx

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