Math Help Forum: Another Integration by Partial Fractions

  1. June 23rd, 2008, 07:20 AM #1
    auslmar
    auslmar is offline
    Junior Member
    Joined
    Jun 2008
    Posts
    46

    Another Integration by Partial Fractions

    Hello,

    \int\frac{-x^2-x-1}{5x^2+7x-6}dx =


    <br /> \int[\frac{A}{5x-3} + \frac{B}{x+2}]dx

    and

    <br /> B(5x-3) + A(x+2) = -x^2-x-1

    I'm having trouble solving A and B. Is there a method for determining them? Or should I be approaching the problem differently altogether?

    Thanks for your consideration,

    Austin Martin
    Follow Math Help Forum on Facebook and Google+

  2. Welcome to Math Help Forum - Click here to Register

    Welcome to the largest Math Help Forum, a free community dedicated to math help and math discussions.

    We welcome everyone and the community is free to join so register today and become part of our math family!

  3. June 23rd, 2008, 07:39 AM #2
    TheEmptySet
    TheEmptySet is offline
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,531
    Thanks
    3
    Quote Originally Posted by auslmar View Post
    Hello,

    \int\frac{-x^2-x-1}{5x^2+7x-6}dx =


    <br /> \int[\frac{A}{5x-3} + \frac{B}{x+2}]dx

    and

    <br /> B(5x-3) + A(x+2) = -x^2-x-1

    I'm having trouble solving A and B. Is there a method for determining them? Or should I be approaching the problem differently altogether?

    Thanks for your consideration,

    Austin Martin
    Since the degree of the numberator and the denominator are the same you need to use long division before partial fractions!

    Remember that if the degree of the numerator is greater than or equal to the denominator ALWAYS use long division.

    I don't know how to write out long division with LaTex but

    \frac{-x^2-x-1}{5x^2+7x-6}=-\frac{1}{5}+\frac{\frac{2}{5}x-\frac{11}{5}}{5x^2+7x-6}=-\frac{1}{5}+\frac{1}{5}\left( \frac{2x- 11}{5x^2+7x-6} \right)

    Now we can use partial fractions on \left( \frac{2x- 11}{5x^2+7x-6} \right)

    Good luck
    Follow Math Help Forum on Facebook and Google+
  4. June 23rd, 2008, 08:55 AM #3
    auslmar
    auslmar is offline
    Junior Member
    Joined
    Jun 2008
    Posts
    46
    Quote Originally Posted by TheEmptySet View Post
    Since the degree of the numberator and the denominator are the same you need to use long division before partial fractions!

    Remember that if the degree of the numerator is greater than or equal to the denominator ALWAYS use long division.

    I don't know how to write out long division with LaTex but

    \frac{-x^2-x-1}{5x^2+7x-6}=-\frac{1}{5}+\frac{\frac{2}{5}x-\frac{11}{5}}{5x^2+7x-6}=-\frac{1}{5}+\frac{1}{5}\left( \frac{2x- 11}{5x^2+7x-6} \right)

    Now we can use partial fractions on \left( \frac{2x- 11}{5x^2+7x-6} \right)

    Good luck
    Ah yes! I completely forgot about the long division bit. Thanks for the help . I'll work it out!
    Follow Math Help Forum on Facebook and Google+
« double integral in vector calculus | Can you Teach Yourself Calculus 2 (Integral) and Calculus 3 (Multivariable) »

Similar Math Help Forum Discussions

  1. Partial fractions for integration
    Posted in the Calculus Forum
    Replies: 6
    Last Post: September 10th, 2011, 10:22 PM
  2. Integration partial fractions
    Posted in the Calculus Forum
    Replies: 6
    Last Post: September 10th, 2011, 02:58 AM
  3. Integration by partial fractions
    Posted in the Calculus Forum
    Replies: 7
    Last Post: March 23rd, 2010, 07:15 AM
  4. integration partial fractions
    Posted in the Calculus Forum
    Replies: 3
    Last Post: June 6th, 2008, 09:58 AM
  5. Integration by partial fractions
    Posted in the Calculus Forum
    Replies: 4
    Last Post: March 8th, 2007, 01:42 PM

/mathhelpforum @mathhelpforum