I would like to compute the following integrations, $$\int\frac{1}{(p-e)^{2}((p-e)^{2}-p^{2})}dp-\int\frac{1}{p^{2}((p-e)^{2}-p^{2})}dp+\int\frac{1}{(p-e)^{2}p^{2}}dp$$ on one side, mathematica tells me that the result is $\log(-1)$, but on the other side, if I add together the integrands the result seems to be equal $0$.
Can someone please explain what goes wrong?
How could it be that integration over real values can yields an imaginary value?
Also, is it true that this integration can yield multiple different values?
