Mathematica vs Wolfram Alpha integration results

Question

When I insert the following integration command in wolframalpha:

int(pi^2*0.05*Exp[-0.1]*14142135/2*x^-1*
  Exp[-x]*y*Exp[-pi*0.1*y^2/2]*
  Hypergeometric2F1[1, 2/3, 5/3, -2*y^-4*(2*10^14)^(3/4)]*
  BesselI[2, x*y*Sqrt[2*pi]],{x,0,0.25},{y,0,Infinity})

I get the following numerical result 6.68805

However, inserting the same command in Mathematica as follows:

NIntegrate[pi^2*0.05*Exp[-0.1]*14142135/2*x^-1*
  Exp[-x]*y*Exp[-pi*0.1*y^2/2]*
  Hypergeometric2F1[1,2/3,5/3,-2*y^-4*(2*10^14)^(3/4)]*
  BesselI[2,x*y*Sqrt[2*pi]],{x,0,0.25},{y,0,Infinity}]

I get the following output (no result)

Am I doing something wrong in Mathematica? Does the wolframalpha site has extended functionality compared to Mathematica (in the above concept).

Thanks in advance

PS: I suppose that wolfralpha translates int() as NIntegrate in the specific case.

Answer 1

I think the apparent answer to your problem is that you entered in Mathematica:

NIntegrate[pi^2 ... blah ]

... and in Mathematica, Pi is the exact real number $\pi$ = 3.1415 ... but pi is just a name like cat or mouse. Capital letters matter. Wolfram Alpha is more flexible about such things, perhaps because it needs to be. This explains why you would get the message about your expression not being numerical, because it contains a pi (or a cat or a dog).