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Math Help - Partial Fractions (I think)

  1. #1
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    Partial Fractions (I think)

    ! = integrate
    I am trying to integrate the following:
    ! x/sqr(a^2-b^2*x^2) dx
    Using partial fractions I get the following:
    1/sqr(2b) ! sqr(x)/sqr(a+bx) dx - 1/sqr(2b) ! sqr(x)/sqr(a-bx) dx.
    This doesn't seem to help at all so it has obviously come off the rails. Could someone be so kind as to show the correct workings?
    Last edited by p75213; March 4th 2010 at 01:57 AM. Reason: I meant partial fractions NOT integration by parts
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  2. #2
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    Just need to know a few things mate.

    1) Is this the equation?

    \dfrac{x}{\sqrt{a^2-b^2x^2}}

    2) Are a and b both constants?
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  3. #3
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    Yes and yes
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  4. #4
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    In which case, I'd consider looking at substitution rather than partial fractions because of that annoying square root.

    Try substituting u = a^2 - b^2x^2 into the equation and integrating that way.
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  5. #5
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    Quote Originally Posted by p75213 View Post
    ! = integrate
    I am trying to integrate the following:
    ! x/sqr(a^2-b^2*x^2) dx
    Using partial fractions I get the following:
    1/sqr(2b) ! sqr(x)/sqr(a+bx) dx - 1/sqr(2b) ! sqr(x)/sqr(a-bx) dx.
    This doesn't seem to help at all so it has obviously come off the rails. Could someone be so kind as to show the correct workings?
    If you use the substitution

    u=a^2-b^2x^2

    then

    \frac{du}{dx}=-2b^2x

    du=-2b^2xdx

    xdx=-\frac{du}{2b^2}

    The integral then is

    -\frac{1}{2b^2}\int{\frac{du}{\sqrt{u}}}
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  6. #6
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    Thanks guys. Easy once you select the correct method. Practice makes perfect.

    Answer is -sqr(a^2-b^2*x^2)/b^2.

    Gojinn: Your right about the ANNOYING square root.
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  7. #7
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    Yeah, those buggers can really make life more tedious. I mean, at first it's kinda handy because if, in my experience, if you see a big square root in the denominator then you'll probably have to use substitution... but once you're over the joy of knowing which technique to use, you realise the extra work you gotta do to find the answer. :P

    Good luck with you other integrals. ^_^
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