   Chapter 7.1, Problem 15E

Chapter
Section
Textbook Problem

# Evaluate the integral. ∫ ( ln x ) 2 d x

To determine

To evaluate: The given integral using the technique of integration by parts.

Explanation

The technique of integration by parts comes in handy when the integrand involves product of two functions. It can be thought of as a rule corresponding to the product rule in differentiation.

Formula used:

The formula for integration by parts in terms of u and v is given by

udv=uvvdu

Given:

The integral, (lnx)2dx.

Calculation:

Make the choice for u and dv such that the resulting integration from the formula above is easier to integrate. Let

u=(lnx)2      dv=dx

Then, the differentiation of u and antiderivative of dv will be

du=2lnxxdx      v=x

Substitute for variables in the formula above to get

(lnx)2dx=(lnx)2xx(2lnxx)dx=(lnx)2x2

### 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

#### Solve the equations in Exercises 126. (x+1)(x+2)2+(x+1)2(x+2)=0

Finite Mathematics and Applied Calculus (MindTap Course List)

#### Evaluate Evaluate the expression. 10. 5|104|

Precalculus: Mathematics for Calculus (Standalone Book)

#### Using a binomial series, the Maclaurin series for is:

Study Guide for Stewart's Multivariable Calculus, 8th

#### True or False: Partial fractions may be used for .

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