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    I have no idea how to go about this.. integrating by parts won't work and I can't think of a substitution.
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    (Original post by StarvingAutist)
    I have no idea how to go about this.. integrating by parts won't work and I can't think of a substitution.
    Limits?
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    (Original post by StarvingAutist)
    I have no idea how to go about this.. integrating by parts won't work and I can't think of a substitution.
    You'll need limits, it doesn't have an antiderivative in terms of elementary functions (other than its trivial Si(x)).
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    (Original post by ODES_PDES)
    Limits?
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    (Original post by StarvingAutist)
    I have no idea how to go about this.. integrating by parts won't work and I can't think of a substitution.
    It's a result in itself.

    https://en.wikipedia.org/wiki/Trigonometric_integral
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    (Original post by StarvingAutist)
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    reverse the order of integration
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    (Original post by ODES_PDES)
    reverse the order of integration
    What should that look like?
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    (Original post by StarvingAutist)
    What should that look like?
    ...
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    (Original post by TeeEm)
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    I didn't realise the sinx / x could go in the y integral; I put it as a limit which obviously didn't help
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    (Original post by StarvingAutist)
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    Start by doing the y integral and it becomes very simple. On another note I did just work out the exact solution to the integral of sinx/x - if someone fancies checking, that would be great.

    \displaystyle\int\frac{sin(x)}{x  }dx = -1 \sum_{i=0}^\infty \frac{n!}{x^{-(n+1)}}\frac{{e^{ix}} + (-1)^ne^{-ix}}{2\sqrt{2}i^ncos(\frac{\pi}{  2}(\frac{2n+1}{2}-1))} + constant
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    (Original post by natninja)
    Start by doing the y integral and it becomes very simple. On another note I did just work out the exact solution to the integral of sinx/x - if someone fancies checking, that would be great.

    \displaystyle\int\frac{sin(x)}{x  }dx = -1 \sum_{i=0}^\infty \frac{n!}{x^{-(n+1)}}\frac{{e^{ix}} + (-1)^ne^{-ix}}{2\sqrt{2}i^ncos(\frac{\pi}{  2}(\frac{2n+1}{2}-1))} + constant
    Looks like you've done far more work that needs to be.

    \displaystyle \sin x = \sum_{n=0}^{\infty} (-1)^n \frac{x^{2n+1}}{(2n+1)!}

    Then divide that by x and integrate term-by-term (skipping over some mild technical justifications).
 
 
 
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