No output in Integration for exponential function?

Questions
1

When I try to do an integration for this function I don’t get a solution, why is it can’t be integrated?
It should be solvable

C2 = -(((1/2)*Subsuperscript[\[Epsilon], c, 11]^2 - a*Subsuperscript[\[Epsilon], c, 11] - k)/
          ((1/2)*a*Subsuperscript[\[Epsilon], c, 11] - 1)) /. Subsuperscript[\[Epsilon], c, 11] -> (1/2)*((r/\[Rho])^C - 1); 
    Integrate[-Exp[-C2], r]

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2

Magdy,

Simplify it first:

In[3]:= Integrate[Simplify[C2], r]

Out[3]= (r (-4 + a + 4 a^2 - (a (r/\[Rho])^C)/(1 + C) - (
   8 (-2 + a^2 (2 + k)) Hypergeometric2F1[1, 1/C, 1 + 1/C, (
     a (r/\[Rho])^C)/(4 + a)])/(4 + a)))/(2 a^2)

Regards,

Neil

3

oops, Sorry I forgot the Exp[] in the expression above. It evidently can’t be integrated in closed form using existing techniques known to Mathematica. I tried Rubi and that failed as well.

Regards,

Neil