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I need to evaluate the following real convergent improper integral using residue theory (vital that i use residue theory so other methods are not needed here) I also need to use the following contour (specifically a keyhole contour to exclude the branch cut):

$$\int_0^\infty \frac{\sqrt{x}}{x^3+1}\ \mathrm dx$$

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    If it is homework just say so :-)2012-03-07
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    Yep i wasnt trying to hide that fact, im new to this forum so im not sure what your policies are, but yes this is homework :)2012-03-07
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    @Bany If you go to the FAQ in the menu, there's a link to the homework FAQ: http://meta.math.stackexchange.com/questions/1803/how-to-ask-a-homework-question2012-03-07
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    @Bany Although it doesn't use contour integration, [this](http://math.stackexchange.com/questions/110457/closed-form-of-integral) answer might help to check the value, which is $\pi/3$2012-03-07
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    Nice picture :)2012-03-07
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    You might be interested in this [Wikipedia example...](http://en.wikipedia.org/w/index.php?title=Methods_of_contour_integration§ion=11#Example_.28IV.29_.E2.80.93_branch_cuts)2012-03-07
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    It could be a lot simpler if we let $ x=u^2$ and avoided dealing with branch cuts at all.2012-03-08

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