   Chapter 7.4, Problem 9E

Chapter
Section
Textbook Problem

# Evaluate the integral. ∫ 5 x + 1 ( 2 x + 1 ) ( x − 1 )   d x

To determine

To evaluate the integral 5x+1(2x+1)(x1)dx

Explanation

Calculation: Given 5x+1(2x+1)(x1)dx,

The partial fraction decomposition of the function is

5x+1(2x+1)(x1)=A2x+1+Bx15x+1=A(x1)+B(2x+1)5x+1=(A+2B)x+(A+B)Equating the coefficients of xandx0,we getA+2B=5,A+B=1on solving for AandB,we getA=1,B=25x+1(2x+1)(

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