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    I'm having trouble seeing the progression from one step to the next. I am just going to type out the line that I don't understand because I think it still makes sense out of context. If I am mistaken about this, let me know and I will post up other relevant information to the question.

    The step is...

    \int_{0}^{\infty} \frac{sinx}{x(1+x^2)} dx = \displaystyle lim_{\epsilon\to0}_{R\to\infty} \int_{\epsilon}^{R} \frac{sinx}{x} dx

    I don't see how the (1 + x^2) part just sort of leaves. I thought I might have made an error in my lecture notes but my friend has the same thing written in her notes.
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    Can you post the full question, or is this part of your proof for the Indentation theorem?
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    I'm pretty sure the two integrals are not equivalent. Looks like something got written down wrong somewhere.
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    (Original post by JoMo1)
    Can you post the full question, or is this part of your proof for the Indentation theorem?

    The full question is \int_0^\infty \frac{sinx}{x(x^2+1)}dx

    The step I'm talking about comes about whilst using the indentation theorem on the small semicircle  \gamma_\epsilon of radius \epsilon to give the modified contour \gamma'. The original contour was the semi-circular contour [-R,R] in the upper-half plane.
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    I was hoping it was some clever step your lecturer had made, seemingly they just forgot to write down the (x^2+1) part of the 2nd part.
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    (Original post by JoMo1)
    I was hoping it was some clever step your lecturer had made, seemingly they just forgot to write down the (x^2+1) part of the 2nd part.
    Oo yep that makes sense. The following question was to do with \frac{sinx}{x} and I didn't realise they were two different questions. Thanks
 
 
 
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