- Thread starter
- #1

\int_{-a}^{a}\frac{dx}{\sqrt{a^2 - x^2}\big(x^2 + b^2\big)},

\quad a,b\text{ real}

\]

So we have poles at \(z = \pm ib\) but are the poles at the integration boundaries included at \(z = \pm a\)?

Should I have

\[

2\pi i \lim_{z\to b}(z - ib)\frac{1}{\sqrt{a^2 - z^2}(z^2 + b^2)} = \frac{\pi}{b\sqrt{a^2 + b^2}}

\]

or if I use the poles at the end points by taking pi i poles real + 2pi i UHP, I get the same answer as above. However, in matheatica, I get

\[

\frac{i\pi}{b\sqrt{a^2 - b^2}}

\]

so I am missing an \(i\) and I have + instead of a -.