I have this simple function but cant seem to have consensus about its cauchy value integral.
I have to integrate it from -1 to 1, and it has a strong singularity on -1. Having that in mind I cant integrate using cauchy method since the singularity is not inside the integration limits. I have tried many things, like quadpack, singularity subtraction, and other methods.
I am suspecting that the value for the integral is either 0 or 0.3217282.
Having in mind that simple techniques failed to resolve this integral what would you try to find the value of the integral ??
Funtion: Integration from -1 to 1 $$ {- 0.0001421026278\,{\frac {\xi\, \left( -1+\xi \right) }{ 0.00625000000+ 0.006250000000\,\xi}}} $$
This is what I got from wolphram alpha:
Taking out the constants, you are trying to evaluate $$\int_{-1}^1 \frac {\xi(\xi-1)}{\xi+1}d\xi$$ This has a logarithmic divergence at $\xi=-1$ and nothing in the numerator to cancel it. There is no finite answer.