deletions | additions       diff --git a/untitled.tex b/untitled.tex  index beb78ea..3f3740d 100644  --- a/untitled.tex  +++ b/untitled.tex 
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\int_{\sigma_R}\frac{dz}{z^{4}+1} &= \int_{\gamma_1}\frac{dz}{z^{4}+1} + \int_{\gamma_2}\frac{dz}{z^{4}+1}\\  &= \frac{\pi i}{-\sqrt2+i\sqrt2} + \frac{\pi i}{\sqrt2+i\sqrt2}\\  &= \frac{\pi i(\sqrt2 + i\sqrt2)+ \pi i(-\sqrt2 + i\sqrt2)}{(-\sqrt2 + i\sqrt2)(\sqrt2 + i\sqrt2)}\\  &= \frac{\pi i(2i\sqrt2)}{-2-2} i(2i\sqrt2)}{-2-2}\\  &= \frac{-2\pi\sqrt2}{-4} \frac{-2\pi\sqrt2}{-4}\\  &= \frac{\pi\sqrt2}{2} \frac{\pi\sqrt2}{2}\\  \end{align*}