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How to write an algorithm that integrates the functions that have singularity points?

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a_ronagh

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How can we write an algorythm to integrate the functions that have some singularity points in the range of integration.
In an analytical form we can use complex plane to map the main integrand to the one contains complex variables and then use the specific methods of the integration of the complex functions (of course if the result of integration diverge to a number),
but I don't know how we can do it in a numerical way in a computer program.
an example of such a function is (sin x/x^2) that we want to integrate in the range (-1 1).
thank you for your help.
 

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