Calculation using Integrate & Plot take too long time & some error

Question

I want to plot this equation.

mu, Eb, gamma, Eg are constant parameters and x is independent parameter.

\[Mu] := 1;
Eb := 0.040;
\[CapitalGamma] := 1;(*Fitting parameter*)
Eg := 2.354
Ebj := Eg - Eb/j^2
c := 1.4 (*fitting parameter*)
A[x_?NumericQ] := \[Mu]^2/x (Sum[(2 Eb /j^3 Sech[(x - Ebj)/\[CapitalGamma]]), {j, 1, 10}] + 
Integrate[Sech[(x - e)/\[CapitalGamma]] 1/(1 - c (e - Eg))(*1/(1-
 E[-2 Pi Sqrt[Eb/(e-Eg)]])*) , {e, Eg, 2.355}])

Plot[A[x], {x, 2.0, 3.5}]

There are two problem.

1. Above the equation, I omit (1/(1-E[-2 Pi Sqrt[Eb/(e-Eg)]])) part because of NIntegrate : non-numerical values error. (maybe divergence issue)
2. Although I omit some part, It takes too long time to Plot.

How remove that error and save calculation time?

Thank you

Answer 1

The Integral has no closed form solution, so use NIntegrate instead of Integrate:

\[Mu] := 1;
Eb := 0.040;
\[CapitalGamma] := 1;(*Fitting parameter*)Eg := 2.354
Ebj := Eg - Eb/j^2
c := 1.4 (*fitting parameter*)

and

A[x_?NumericQ] := \[Mu]^2/
   x (Sum[(2 Eb/j^3 Sech[(x - Ebj)/\[CapitalGamma]]), {j, 1, 10}] + 
    NIntegrate[Sech[(x - e)/\[CapitalGamma]] 1/(1 - c (e - Eg))(*1/(1-
     E[-2 Pi Sqrt[Eb/(e-Eg)]])*), {e, Eg, 2.355}])

then

Plot[A[x], {x, 2.0, 3.5}]

delivers: