Exponential Integral Solution

Integrate[ Exp[-x] - Exp[-x - b*Sqrt[-a + x^2]], {x, Sqrt[a], Infinity}]


If anyone has mathematica pro, can i please get the solution to this integral? a and b are real positive numbers

• What is MathematicaPro? I never heard about it. – zhk Apr 13 '17 at 5:20

I think this integral isn't solveable. MMA Version 8.0 can't do neither the definite integral nor the indefinite one. Also the rule-based-integrator of Albert Richt (http://www.apmaths.uwo.ca/~arich/ ) can't do it. Therefore it remains numerical integration

    int[a_, b_] :=
NIntegrate[
Exp[-x] - Exp[-x - b*Sqrt[-a + x^2]], {x, Sqrt[a], Infinity}]

Plot3D[int[a, b], {a, 0, 11}, {b, 0, 13},
AxesLabel -> {a, b, NIntegrate}, PlotRange -> All]


• Thanks, Can u recommend specific numerical integration method? @Akku14 – hakkunamattata Apr 14 '17 at 4:56
• @Kanwal Zaidi The function to integrate here makes no problems, therefore you can leave Mathematica the automatic choise of the integration method like I did above with NIntegrate. – Akku14 Apr 14 '17 at 18:21