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Partial fraction problem

  • #1

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
 

Answers and Replies

  • #3
Curious3141
Homework Helper
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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:

[tex]\frac { 18 }{ (x^{ 2 }+9)(x-3) } =\frac { Ax+B }{ x^{ 2 }+9 } +\frac { C }{ x-3 } [/tex]

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

Then just subtract the [itex]\frac { C }{ x-3 } [/itex] from the LHS and simplify to find the remaining term.
 
  • #4
The general form for the PF decomposition would be:

[tex]\frac { 18 }{ (x^{ 2 }+9)(x-3) } =\frac { Ax+B }{ x^{ 2 }+9 } +\frac { C }{ x-3 } [/tex]

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

Then just subtract the [itex]\frac { C }{ x-3 } [/itex] from the LHS and simplify to find the remaining term.
ok yeah I figured it out thanks.
 

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