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Math Help - A Integration problem..:S

  1. #1
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    A Integration problem..:S

    Hallo to all, i have a problem with calculating a integral, i tried it with substitution and partial integration, but had no luck. Please help if someone have an idea. Thank you!
    The result is one of the following:
    a) 1
    b) 2
    c) ln 2
    d) 1/4 *ln 5
    4) 1/2 * ln 3

    (the problem is described in the picture)

    A Integration problem..:S-integral.jpg
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  2. #2
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    The bounds for the integral in the picture are incorrect - are you sure that's the correct problem?
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  3. #3
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    Integration by parts works for me. Use \mbox{Ei} (-x) =\int_{-\infty}^x \dfrac{e^{-x}}{x}\, dx

    Edit
    Ei is the exponential integral
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  4. #4
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    i tought also that it is incorrect but it was written so in my college exam.
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  5. #5
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    This is what I get.

    \int_0^x \dfrac{e^{-x}\sin^2 x}{x}\, dx=\dfrac{1}{2}\mbox{Ei}(-x)-\dfrac{1}{4}\mbox{Ei}(-(1+2i)x)-\dfrac{1}{4}\mbox{Ei}((-1+2i)x)+\dfrac{1}{4}\ln 5
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