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May I seek assistance on how this integral can be evaluated?

$\int_{\Sigma} \frac{dydz}{[a_{o}(y^{2}+z^{2})+2f_{o}y+2g_{o}z+c_{o}]^{2}}$ where $a_{o}c_{o}-f_{o}^{2}-g_{0}^{2}=\frac{1}{4}$

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  • $\begingroup$ Is $\Sigma$ a rectangular region? $\endgroup$ – David H Nov 9 '18 at 2:00
  • $\begingroup$ Yes of course. I'm asking if we may assume that region is rectangular. $\endgroup$ – David H Nov 9 '18 at 3:43
  • $\begingroup$ @DavidH, yes, the region is rectangular. $\endgroup$ – Bryan London Nov 9 '18 at 4:04
  • $\begingroup$ Also, I just noticed the $y^z$ term in the denominator. Are you sure this isn't perhaps a typo, and should be $y^2$? $\endgroup$ – David H Nov 9 '18 at 4:53
  • $\begingroup$ @DavidH, thanks for pointing this out. Yes, it is indeed a typo. I had corrected my initial post. $\endgroup$ – Bryan London Nov 9 '18 at 5:19

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