   Chapter 6.1, Problem 10E ### 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 5-16, use integration by parts to find the indefinite integral, See Examples 1, 2, 3, and 4. ∫ ln ( 3 x ) 2   d x

To determine

To calculate: The value of indefinite integral ln(3x)2dx.

Explanation

Given Information:

The provided indefinite integral is ln(3x)2dx.

Formula used:

The integration by parts udv=uvvdu.

Where, u and v are function of x.

kdx=kx+C

Calculation:

Consider the indefinite integral ln(3x)2dx

The above indefinite integral can be written as,

ln(3x)2dx=ln(9x2)dx=ln(9)dx+2lnxdx

Use integration by parts on the second integral 2lnxdx

Here,

dv=dx and u=lnx

First find v,

dv=dxdv=dx

On further solving,

v=x …...…... (1)

Find du:

u=lnx

Differentiate both side with respect x;

dudx=d(lnx)dxdudx=1x

And,

du=1xdx …...…... (2)

Apply integration by parts on the second integral 2lnxdx and substitute equation (1) and (2) in udv=uvvdu,

ln(3x)2dx=ln(9)dx+2lnxdx=ln(9)dx+2[xlnxx1xdx<

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Evaluate the limit. limx1+(xx11lnx)

Single Variable Calculus: Early Transcendentals, Volume I

#### In Exercises 21-24, find the distance between the given points. 24. (2, 1) and (10, 6)

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### In Problems 47-50, rationalize the denominator of each fraction and simplify. 50.

Mathematical Applications for the Management, Life, and Social Sciences

#### If f(x) = sin 2x, an upper bound for |f(n + 1)(x)| is 2 2n 2n + 1 22n

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

#### The third partial sum of is:

Study Guide for Stewart's Multivariable Calculus, 8th 