Partial Fraction Decomposition for ∫18/((x2+9)(x-3))

[charmedbeauty]

Homework Statement

Find ∫18/((x²+9)(x-3))

Homework Equations

The Attempt at a Solution

Im a little stuck on this.

18∫1/((x²+9)(x-3))

Im not sure how to turn this into a partial fraction.. help.

Thanks

 

[Simon Bridge]

You understand $$\frac{a+b}{ab} =\frac{1}{a}+\frac{1}{b}$$ ... then expand the concept for functions.
http://www.math.ucdavis.edu/~kouba/CalcTwoDIRECTORY/partialfracdirectory/PartialFrac.html

 

[Curious3141]

Homework Statement

Find ∫18/((x²+9)(x-3))

Homework Equations

The Attempt at a Solution

Im a little stuck on this.

18∫1/((x²+9)(x-3))

Im not sure how to turn this into a partial fraction.. help.

Thanks

The general form for the PF decomposition would be:

$$\frac { 18 }{ (x^{ 2 }+9)(x-3) } =\frac { Ax+B }{ x^{ 2 }+9 } +\frac { C }{ x-3 }$$

First find C by using the Heaviside coverup rule (put x = 3 after multiplying both sides by (x-3).

Then just subtract the $\frac { C }{ x-3 }$ from the LHS and simplify to find the remaining term.

 

[charmedbeauty]

The general form for the PF decomposition would be:

$$\frac { 18 }{ (x^{ 2 }+9)(x-3) } =\frac { Ax+B }{ x^{ 2 }+9 } +\frac { C }{ x-3 }$$

First find C by using the Heaviside coverup rule (put x = 3 after multiplying both sides by (x-3).

Then just subtract the $\frac { C }{ x-3 }$ from the LHS and simplify to find the remaining term.

ok yeah I figured it out thanks.