   Chapter 7.4, Problem 20E

Chapter
Section
Textbook Problem

# Evaluate the integral. ∫ 2 3 x ( 3 − 5 x ) ( 3 x − 1 ) ( x − 1 ) 2 d x

To determine

To evaluate the integral 23x(35x)(3x1)(x1)2dx

Explanation

Calculation: Given 23x(35x)(3x1)(x1)2dx

Resolving into partial fractions,

x(35x)(3x1)(x1)2=A3x1+B(x1)+C(x1)2x(35x)=A(x1)2+B(3x1)(x1)+C(3x1)5x2+3x=(A+3B)x2+(2A4B+3C)x+(A+BC)comparing coefficients of x2,xandx0A+3B=5,2A4B+3C=3,A+BC=0A=1,B=2,C=1x(35x)(3x1)(x1)2=13x12(x1)1(x1)2

Therefore

23

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