Chapter 8.5, Problem 12E

### 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 ( x − 2 ) 2 d x

To determine

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

Explanation

Given:

The integral function is âˆ«5xâˆ’2(xâˆ’2)2dx.

Formula used: âˆ«1xdx=lnx+C.

Calculation:

Consider the following indefinite integral,

âˆ«5xâˆ’2(xâˆ’2)2dx

Now use partial fraction method, to get,

5xâˆ’2(xâˆ’2)2dx=Axâˆ’2+B(xâˆ’2)25xâˆ’2=A(xâˆ’2)+B

Calculate value of A and B

At x=2,

5(2)âˆ’2=A(2âˆ’2)+BB=8

At x=0,

5(0)âˆ’2=A(0âˆ’2)+Bâˆ’2A+B=âˆ’2âˆ’2A+8=âˆ’2A<

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