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Avoid long output, Real variables?


Is it possible to tell Mathematica that a variable, x, is Real?
I am looking for commands like those of some competing vendor: 
  assume(x, real)
  assume(x>0)
If I cannot declare x to be Real, I get clumsy answers. For
instance, a Fourier transform which for real x is just:

  2 BesselK[0, x Sign[x]]

gives me instead a pretty long answer where the actual solution
for real x is hardly recognizable between the rest:

  In[4]:=Integrate[E^(I*k*x)/Sqrt[1+k^2]/(2*Pi), {k,-Infinity,Infinity}]

  Out[4]= If[Im[x] == 0, 2 BesselK[0, x Sign[x]], 
 
                    I k x
                   E
      Integrate[------------, {k, -Infinity, Infinity}]] / (2 Pi)
                          2
                Sqrt[1 + k ]
  In[5]:=

And it can get worse if several variables are involved. So I really
hope that someone can teach me how to declare them Real (or positive).

Thanks in advance,
Jos




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