   Chapter 8.5, Problem 26E

Chapter
Section
Textbook Problem

# Evaluating a Definite Integral In exercises 21-24, use partial fractions to evaluate the definite integral. Use a graphing utility to verify your result. ∫ 0 1 x 2 − x x 2 + x + 1 d x .

To determine
The value of given definite integral by using partial fractions.

Explanation

Given:

The definite integral is 01x2xx2+x+1dx.

Formula used:

1xdx=ln|x|+C.

Calculation:

Consider the following definite integral,

01x2xx2+x+1dx.

The above integral function can be written as,

Adding and subtracting 2x+1 to the numerator

x2x+2x+12x1x2+x+1 x2x+2x+1x2+x+1+2x1x2+x+1x2xx2+x+1=x2+x+1x2+x+12x+1x2+x+1=12x+1x2+x+1

Simplify further,

01x2xx2+x+1dx=01(12x+1x2+x+1)dx

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