   Chapter 8.5, Problem 19E

Chapter
Section
Textbook Problem

# Using Partial Fractions In Exercises 3-20, use partial fractions to find the indefinite integral. ∫ x 2 x 4 − 2 x 2 − 8   d x

To determine

To calculate: The solution of the indefinite integral x2x42x28dx is. Make use of partial fractions.

Explanation

Given:

The indefinite integral is x2x42x28dx.

Formula used:

1a2+x2dx=1aarctan(xa)+c

Calculate:

Consider,

x2x42x28dx

By partial fraction,

x2x42x28=Ax2+Bx+2+Cx+Dx2+2 …… (1)

So,

(x2)(x+2)(x2+2)x2x42x28dx=(Ax2+Bx+2+Cx+Dx2+2)(x2)(x+2)(x2+2)x2=A(x+2)(x2+2)+B(x2)(x2+2)+(Cx+D)(x2)(x+2)

Put x=2,

4=A(4)(6)4=A(24)A=16

Put x=2,

4=B(4)(6)4=B(24)B=16

Put x=0,

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