The following code yields the correct result:



Another interesting fact is that if I omit the assumption that k ∈ Reals, then Mathematica still gets it right, but it takes ~3x more time:



What is puzzling though is that if I use Assumptions with Integrate I don't get the expected result:



I was under the impression that Assuming[{a1,a2,...}, Integrate[...]] was equivalent to Integrate[..., Assumptions -&gt; a1 &amp;&amp; a2 &amp;&amp; ...]. 

Could anyone please try to reproduce my results, ideally in a different OS/Mathematica version combination ? That is something other than Mathematica 9.0.1/Mac OSX 10.9 ? 

Calculate integral for arbitrary parameter n in infinite square well problem
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