Re: Solving special exponential integral

*To*: mathgroup at smc.vnet.net*Subject*: [mg132308] Re: Solving special exponential integral*From*: "Alexander Elkins" <alexander_elkins at hotmail.com>*Date*: Fri, 7 Feb 2014 08:07:27 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-outx@smc.vnet.net*Delivered-to*: mathgroup-newsendx@smc.vnet.net*References*: <lckihv$1hc$1@smc.vnet.net>

Using the variable substitution a -> Sqrt[x - b] represented here by the function g, Mathematica gives the following result: In[1]:= With[{f = Function[a, E^(-((a^2 * b * c^2)/(a^2 + b)))/(a^2 + b)^2], g = Function[x, Sqrt[x - b]]}, Integrate[ f[g[x]] D[g[x], x], {x, Sequence @@ InverseFunction[g] /@ {0, Infinity}}]] Out[1]= ConditionalExpression[( E^(-((b c^2)/ 2)) \[Pi] (BesselI[0, (b c^2)/2] + BesselI[1, (b c^2)/2]))/( 4 b^(3/2)), Re[c^2] < 0 && b > 0] Perhaps this helps... "simone8888" <stefanvuckovic1 at gmail.com> wrote in message news:lckihv$1hc$1 at smc.vnet.net... > I have tried to solve this integral: > > Integrate[E^(-((a^2 b c^2)/(a^2 + b)))/(a^2 + b)^2,a] > Mathemathica is not able to solve it, I have tried the integration by parts and it did not work, as well as some substitutions. Any idea how to tackle this problem? >