   Chapter 8.5, Problem 9E

Chapter
Section
Textbook Problem

# Using Partial Fractions In Exercises 3-20, use partial fractions to find the indefinite integral. ∫ x 2 + 12 x + 12 x 3 − 4 x d x

To determine

To calculate: The indefinite integral for the given function, by using partial fractions.

Explanation

Given:

The integral function is x2+12x+12x3+4xdx.

Formula used:

1xdx=lnx+C.

Calculation:

Consider following indefinite integral,

x2+12x+12x3+4xdx

The above integral function can be written as,

x2+12x+12x34x=x2+12x+12x(x24)=x2+12x+12x(x+2)(x2)

Now by using partial fraction method we get,

x2+12x+12x(x+2)(x2)=Ax+Bx+2+Cx2x2+12x+12=A(x+2)(x2)+Bx(x2)+Cx(x+2)

By simplifying further we get,

At x=0,

(0)2+12(0)+12=A(0+2)(02)+B(0)(02)+C(0)(0+2)A=3

At x=2,

(2)2+12(2)+12=A(2+2)(22)+B(2)(22)+C(2)(2+2)C=5

At x=2,

(

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