I want to compute
$$ \int_{-\infty}^{\infty} \frac{1}{\sqrt{x+yi +2}} dy $$ where $i$ is the imaginary number. How to compute this integral??
2026-04-03 05:53:39.1775195619
Integral with complex variable
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Hint: $$ \int_{-\infty}^{\infty} \frac{1}{\sqrt{x+yi +2}} dy = \int_{-\infty}^{\infty} \frac{1}{\sqrt{x+yi +2}}\frac{\sqrt{x+2-iy}}{\sqrt{x+2-iy}}dy=... $$