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Math Help - Integration partial fractions

  1. #1
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    Arrow Integration partial fractions

    Hello,
    could someone tell me where I made a mistake on this partial fraction problem
    Please
    Last edited by wolfhound; February 28th 2010 at 08:29 AM. Reason: wrong picture
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  2. #2
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    Quote Originally Posted by wolfhound View Post
    Hello,
    could someone tell me where I made a mistake on this partial fraction problem
    Please
    hi wolfhound,

    \frac{A}{x}+\frac{B}{x^2+1}=\frac{1}{x^3+x}

    \frac{A\left(x^2+1\right)+Bx}{x\left(x^2+1\right)}  =\frac{1}{x^3+x}

    \frac{Ax^2+A+Bx}{x^3+x}=\frac{1}{x^3+x}

    x\left(Ax+B\right)+A=x(0)+1

    A=1

    (1)x+B=0\ \Rightarrow\ B=-x
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  3. #3
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    Hi archie
    Oh so I dont actually get a value for B? except B=-x?
    someone said I should input i in to solve these also
    when should I take a coefficient as x and not a value please?
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  4. #4
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    Hi wolfhound,

    sometimes there will be an x-component of the A and B values.
    They are not necessarily "constants".

    They are "numerators".

    They only end up being constants sometimes.

    If you add those two resulting fractions together,
    you will see that the result is the original fraction you wanted to integrate.

    since the sum of the resulting fractions is the original,
    you can more conveniently integrate the partial fractions.

    The trick is....

    if the numerator of the original fraction is a constant,
    then you can write it as "constant + (0)x"
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  5. #5
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    Thumbs up

    I see,
    I am going to practice some more now
    Thanks
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