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Help with an integral

  1. Apr 2, 2004 #1
    Could someone please help me integrate

    [tex]\int \frac { dx } { ( a + x )^2 + sin^{2} ( \pi x ) } [/tex]

    where a is just an arbitrary constant...

    Thanks in advance...
    Last edited by a moderator: Apr 2, 2004
  2. jcsd
  3. Apr 2, 2004 #2
    Oh my. That is ugly.

    What kind of evil person is making you do that?

  4. Apr 3, 2004 #3
    The Integrator can't do it, therefore it's impossible. (I know this isn't true, but when Mathematica can't do it I get kind of scared.)


    It just spits this out: http://integrals.wolfram.com/graphics.cgi?format=StandardForm&FontSize=Medium&expr=1/Sqrt%5B%28a%2Bx%29%5E2%20%2B%20%28Sin%5BPi%2Ax%5D%29%5E2%5D [Broken]
    Last edited by a moderator: May 1, 2017
  5. Apr 3, 2004 #4


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    Maple 8 says it cannot be done.
    No answer I guess.
  6. Apr 3, 2004 #5


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    Homework Helper

    I can never get that to do a difficult integration when I have one. But yes this does look like a really nasty one.

    Edit: I put it in and got this: http://integrals.wolfram.com/graphics.cgi?format=StandardForm&FontSize=Medium&x=24&expr=1%20/%20%28%20%28a%20%2B%20x%29%5E2%20%2B%20sin%5E2%28%28Pi%29x%29%20%29&y=21 [Broken]
    Last edited by a moderator: May 1, 2017
  7. Apr 3, 2004 #6
    Both my version of Mathematica and the Integrator return the integral.

    The first one you had, MathNerd, Mathematica could do, but this new one doesn't work out.

  8. Apr 4, 2004 #7
    How do you get a sin^2 with no argument?
    Last edited by a moderator: May 1, 2017
  9. Apr 4, 2004 #8
    U can calculate for certain sets of values of x where sin(pi x)=0 or 1
  10. Apr 4, 2004 #9
    Yeah, really. The integral of a constant is a piece of cake.

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