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Partial fractions

  • Thread starter arl146
  • Start date
  • #1
343
1

Homework Statement


determine the indefinite integral: ∫ (4x+10)/(9x^2+24x+16) dx


Homework Equations


partial fractions technique


The Attempt at a Solution



i know it's partial fractions and i thought i did it right but i got the wrong answer.

(4x+10)/(9x^2+24x+16) = (4x+10)/(3x+4)^2 = A/(3x+4) + B/(3x+4)^2
is that part right before I continue?
 

Answers and Replies

  • #2
Ray Vickson
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Homework Helper
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Homework Statement


determine the indefinite integral: ∫ (4x+10)/(9x^2+24x+16) dx


Homework Equations


partial fractions technique


The Attempt at a Solution



i know it's partial fractions and i thought i did it right but i got the wrong answer.

(4x+10)/(9x^2+24x+16) = (4x+10)/(3x+4)^2 = A/(3x+4) + B/(3x+4)^2
is that part right before I continue?
Yes, that is the right idea.

RGV
 
  • #3
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390
Yes, that's right.
 
  • #4
HallsofIvy
Science Advisor
Homework Helper
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Homework Statement


determine the indefinite integral: ∫ (4x+10)/(9x^2+24x+16) dx


Homework Equations


partial fractions technique


The Attempt at a Solution



i know it's partial fractions and i thought i did it right but i got the wrong answer.

(4x+10)/(9x^2+24x+16) = (4x+10)/(3x+4)^2 = A/(3x+4) + B/(3x+4)^2
is that part right before I continue?
As others have told you that is correct. Now multiply both sides by (3x+4)^2 to get (4x+10)(3x+ 4)^2= A(3x+ 4)+ B. Taking x= -4/3 gives an easy solution for B. Take x to be any other number, say, x= 0, to get an equation for A.
 
  • #5
343
1
ohhhh .. i see what i did. ok .. so i was doing A(3x+ 4)^2 + B(3x+4) not realizing the denominator difference. stupid mistake. thanks!
 

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