   Chapter 8.5, Problem 36E ### 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
1 views

# Integration by Parts In Exercises 33-38, use integration by parts to find the indefinite integral. ∫ 4 x   csc 2   x   d x

To determine

To calculate: The integral of 4xcsc2xdx.

Explanation

Given Information:

The provided integral is 4xcsc2xdx.

Formula used:

Write the formula used in integration by parts method.

pqdx=pqdxp(qdx)dx

Here, p=p(x) and q=q(x)

Write the formula of integral of csc2u.

csc2udu=cotu+C

Write the formula of integral of cotu.

cotudu=ln|sinu|+C

The provided integral is,

4xcsc2xdx

Use the formula of integration by parts to find integral of above expression.

4xcsc2xdx=4xcsc2xdxddx4x(csc2xdx)dx=4xsec2xdx4(csc2xdx)dx

Here, p=4x and q=csc2x

Let u=x

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