   Chapter 8.5, Problem 12E

Chapter
Section
Textbook Problem

Using Partial Fractions In Exercises 3-20, use partial fractions to find the indefinite integral. ∫ 5 x − 2 ( x − 2 ) 2 d x

To determine

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

Explanation

Given:

The integral function is 5x2(x2)2dx.

Formula used: 1xdx=lnx+C.

Calculation:

Consider the following indefinite integral,

5x2(x2)2dx

Now use partial fraction method, to get,

5x2(x2)2dx=Ax2+B(x2)25x2=A(x2)+B

Calculate value of A and B

At x=2,

5(2)2=A(22)+BB=8

At x=0,

5(0)2=A(02)+B2A+B=22A+8=2A<

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