   Chapter 7.4, Problem 28E

Chapter
Section
Textbook Problem

# Evaluate the integral. ∫ x 3 + 6 x − 2 x 4 + 6 x 2 d x

To determine

Toevaluate the integral x3+6x2x4+6x2dx

Explanation

Calculation: Given x3+6x2x4+6x2dx

Factor the denominator x4+6x2=x2(x2+6)

Partial factor Decomposition is given by

x3+6x2x2(x2+6)=Ax+Bx2+Cx+Dx2+6

x3+6x2x2(x2+6)=Ax(x2+6)+B(x2+6)+(Cx+D)x2x2(x2+6)

x3+6x2=Ax(x2+6)+B(x2+6)+(Cx+D)x2

x3+6x2=Ax3+6Ax+Bx2+6B+Cx3+Dx2

Group like-terms then factor

x3+6x2=(Ax3+Cx3)+(Bx2+Dx2)+6Ax+6B

x3+6x2=(A+C)x3+(B+D)x2+6Ax+6B

Rewrite x3+6x2 as (1)x3+(0)x2+6x2

x3+6x2=(A+C)x3+(B+D)x2+6Ax+

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