Chapter 8, Problem 40RE

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 37–44, use partial fractions to find the indefinite integral. ∫ 4 x − 2 3 ( x − 1 ) 2 d x

To determine

To calculate: The integral 4x23(x1)2dx using partial fractions.

Explanation

Given:

The integral 23âˆ«2xâˆ’1(xâˆ’1)2dx

Formula Used:

In partial fraction, for integral of type

âˆ«x+a(x+b)2dx, it can be simplified as

x+a(x+b)2=A(x+b)+B(x+b)2

Calculation:

Here the integral is 23âˆ«2xâˆ’1(xâˆ’1)2dx.

Thus, 23âˆ«2xâˆ’1(xâˆ’1)2dx can be written as

2xâˆ’1(xâˆ’1)2=Axâˆ’1+B(xâˆ’1)22xâˆ’1(xâˆ’1)

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