title: How to overcome singularities in numerical integration (in Matlab or Mathematica)
body: <p>I want to numerically integrate the following:</p>
  
  <p><img src="https://i.stack.imgur.com/rwyBQ.gif" alt="eq1"></p>
  
  <p>where</p>
  
  <p><img src="https://i.stack.imgur.com/aFCQI.gif" alt="eq2"></p>
  
  <p>and <code>a</code>, <code>b</code> and <code>β</code> are constants which for simplicity, can all be set to <code>1</code>.</p>
  
  <p>Neither Matlab using <code>dblquad</code>, nor Mathematica using <code>NIntegrate</code> can deal with the singularity created by the denominator. Since it's a double integral, I can't specify where the singularity is in Mathematica. </p>
  
  <p>I'm sure that it is not infinite since this integral is based in perturbation theory and without the </p>
  
  <p><img src="https://i.stack.imgur.com/AMfRP.gif" alt="enter image description here"> </p>
  
  <p>has been found before (just not by me so I don't know how it's done).</p>
  
  <p>Any ideas?</p>