Chapter 8.5, Problem 15E

### 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

# Using Partial Fractions In Exercises 3-20, use partial fractions to find the indefinite integral. ∫ 9 − x 2 7 x 3 + x d x

To determine

To calculate: The indefinite integral for the given function, by using partial fractions.

Explanation

Given:

The integral function is âˆ«9âˆ’x27x3+xdx.

Formula used:

âˆ«1xdx=ln|x|+C.

Calculation:

Consider the following indefinite integral,

âˆ«9âˆ’x27x3+xdx

The above integral function can be written as,

9âˆ’x27x3+x=9âˆ’x2x(7x2+1)

Now by using partial fraction method we get,

9âˆ’x2x(7x2+1)=Ax+Bx+C7x2+19âˆ’x2=A(7x2+1)+(Bx+C)(x)9âˆ’x2=(7A+B)x2+Cx+A

By solving further we get,

A=9,C=0 And 7A+B=âˆ’1Â

Solve the above equation for B

7(9)+B=âˆ’1B=âˆ’64

So by substituting the value of A, B and C we get,

9âˆ’x2x(7x2+1)=9x+âˆ’64x+07x2+1.......

### 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

#### In Exercises 516, evaluate the given quantity. log1,000

Finite Mathematics and Applied Calculus (MindTap Course List)

#### In Problems 7-34, perform the indicated operations and simplify. 14.

Mathematical Applications for the Management, Life, and Social Sciences

#### True or False: n=1an converges if and only if limnan=0.

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

#### Describe the elements of an abstract.

Research Methods for the Behavioral Sciences (MindTap Course List)