   Chapter 8.2, Problem 7E

Chapter
Section
Textbook Problem

# Using Integration by Parts In Exercises 11-14, find the indefinite integral using integration by parts with the given choices of u and dv. ∫ x 3 ln x d x : u = ln x , d v = x 3   d x

To determine

To calculate: The expression of the indefinite integral given as, x3lnxdx will be by making use of integration by parts.

Explanation

Given:

The required expressions of u and dv for integration by parts are: u=lnx and dv=x3.

Formula used:

The formula for integration by parts:

udv=uvvdu

Calculation:

Since dv=x3dx.

Now, integrate both the sides and find v.

v=x3dx=x44

And u=lnx.

Now, differentiate both the sides and find du.

dudx=ddx(lnx)dudx=1xdu=1xdx

Now, consider the given integral and apply the integration by parts and substitute the values

### 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 