   Chapter 7.4, Problem 25E

Chapter
Section
Textbook Problem

# Evaluate the integral. ∫ 4 x x 3 + x 2 + x + 1 d x

To determine

To evaluate the integral 4xx3+x2+x+1dx

Explanation

Calculation: Given 4xx3+x2+x+1dx

Resolve into partial fractions

4xx3+x2+x+1=4xx2(x+1)+(x+1)=4x(x2+1)(x+1)=Ax+1+Bx+Cx2+14x=A(x2+3)+(Bx+C)(x+1)=(A+B)x2+(B+C)x+(3A+C)on solving , we getA+B=0,B+C=4,3A+C=0A=1,B=1,C=34xx3+x2+x+1=1x+1+x+3x2+1=1x+1+xx2+1+

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