   Chapter 8.5, Problem 33E

Chapter
Section
Textbook Problem

# Finding an Indefinite Integral In Exercises 25-32, use substitution and partial fractions to find the indefinite integral. ∫ x x − 4   d x

To determine

To calculate: The solution of the indefinite integral xx4dx. Make use of partial fractions.

Explanation

Given:

The indefinite integral xx4dx

Formula used:

Integration identity 1udu=ln(u)+c and the logarithmic property ln|a|ln|b|=ln|ab|.

Calculation:

Consider integral function,

xx4

Multiply the numerator and denominator by x,

xx4=xx4(xx)=xx(x4)

Put,

u=xdu=12xdx

Therefore,

xx4dx=xx(x4)dx=u2u24(2)du=2u2duu24

Subtract and add 4, then separate the numerator,

2u2duu24=2u24+4u24du=2(u24u24+4u24)du=2(1+4u24)du

Simplify 4u24 by using partial fraction,

4u24=4(u2)(u+2)=Au

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