Chapter 8.2, Problem 26E

Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

Finding an Indefinite Integral In Exercises 15–34, find the indefinite integral. ( Note: Solve by the simplest method–not all require integration by parts.) ∫ 2 x 1 − 6 x   d x

To determine

To calculate: The indefinite integral 2x(16x)dx by using the simplest method.

Explanation

Given: âˆ«2x(1âˆ’6x)dx

Formula used:

The formula for integral by part:

âˆ«I.IIdx=Iâˆ«IIdxâˆ’âˆ«(ddxI.âˆ«IIdx)â€‰dx

Calculation:

Let I=xÂ andÂ II=(1âˆ’6x)âˆ’12.

The formula for integral by part is

âˆ«I.IIdx=Iâˆ«IIdxâˆ’âˆ«(ddxI.âˆ«IIdx)â€‰dx

Now, apply this method and find integration:

âˆ«2x(1âˆ’6x)dx=2[xâˆ«(1âˆ’6x)âˆ’12dxâˆ’âˆ«(ddxxâˆ«(1âˆ’6x)âˆ’12dx)dx]=2[x(1âˆ’6x)1âˆ’1212Ã—(âˆ’6)âˆ’âˆ«(1âˆ’6x)1âˆ’12<

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