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Partial fractions

  1. Sep 19, 2012 #1
    1. The problem statement, all variables and given/known data
    determine the indefinite integral: ∫ (4x+10)/(9x^2+24x+16) dx

    2. Relevant equations
    partial fractions technique

    3. 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?
  2. jcsd
  3. Sep 19, 2012 #2

    Ray Vickson

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    Yes, that is the right idea.

  4. Sep 19, 2012 #3
    Yes, that's right.
  5. Sep 19, 2012 #4


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    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.
  6. Sep 19, 2012 #5
    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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