Hi everyone,(adsbygoogle = window.adsbygoogle || []).push({});

I would like to calculate the following integral:

[itex]P\int_0^{\pi}\frac{1}{cos(x)-a}dx[/itex], with [itex]

|a|\leq 1[/itex].

The 'P' in front stands for the so-called Cauchy Principle value.

Whenever a is not in the specified domain, the integrand does not have a pole and one can do the integration immediately (I have Maple computed it for me).

However, when a is in the above domain, the denominator can become zero and one has to integrate through the pole, hence the P.

But, I don't know how to do this in practice.

They say just cut out a piece of size delta before and after the pole and just do the integration. Than take the proper limits.

But, can the same rules be applied as wouldnt a have been in this domain. Is it allowed to use the same techniques as without any poles in the integrand?

Otherwise, are there any other techniques, tricks ... ?

Many thanks in advance.

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# Integral with Cauchy Prinicpal value

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