Chapter 8.5, Problem 5E

### 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. ∫ 5 x 2 + 3 x − 4 d x

To determine

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

Explanation

Given:

The integral function is âˆ«5x2+3xâˆ’4dx.

Formula used: âˆ«1xdx=lnx+C.

Calculation:

Consider the following indefinite integral,

âˆ«5x2+3xâˆ’4dx

By factorizing denominator of the integral function we get

x2+3xâˆ’4=x2+4xâˆ’xâˆ’4=x(x+4)âˆ’1(x+4)=(xâˆ’1)(x+4)

So,

âˆ«5x2+3xâˆ’4dx=5(xâˆ’1)(x+4)

Now by using partial fraction method we get,,,

5(xâˆ’1)(x+4)=âˆ’1x+4+1xâˆ’1 5(xâˆ’1)(x+4)=Ax+4+Bxâˆ’15=A(xâˆ’1)+B(x+4)(xâˆ’1)(x+4

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