Multiple plots on same graph for different parameter?

Question

I would like to be able to Plot a function (with an implicit Integrate command) with various values for a certain parameter (phi in the code below for values 0.01 and 0.02) all on the same Plot to compare.Below is my code:

e = 1.60217657*10^-19;
n = 10^-9/e;
R = 1.5;
sigma = 50*10^-6;
p = (R*phi^3)/(24 sigma);
g = D[Exp[-((curlEprime)^2/2)], curlEprime];

G = p^(-(1/3)) (Exp[-((curlE - p)^2/2)] - Exp[-((curlE - 4 p)^2/2)]) +
Integrate[1/(curlE - curlEprime)^(1/3) g, {curlEprime, curlE - p, curlE}];

de = (2 e^2 n)/(3^(1/3) Sqrt[2 Pi] R^(2/3) sigma^(4/3)) G

Plot[de, {curlE, -10, 10}] /. phi -> {0.01, 0.02}

Answer 1

Below you'll find a slightly changed version of your code (note the new definition of g - saves some space). Basically, as Öskå wrote in his comments above, you need to define functions of phi, curlEprime and curlE. Also, it seems that the integral could not be derived in a symbolic way.

Furthermore, you should not name your variable with capital letters (see here), hence the small changes bellow:

e = 1.60217657*10^-19;
n = 10^-9/e;
r = 1.5;
sigma = 50*10^-6;
p[phi_] := (r*phi^3)/(24 sigma);
g[curlEprime_] := Exp[-((curlEprime)^2/2)];

gSomething[phi_, curlE_] := With[{p = p[phi]}, 
  p^(-(1/3)) (g[curlE - p] - g[curlE - 4 p]) + 
  NIntegrate[1/(curlE - curlEprime)^(1/3)  g'[curlEprime], 
    {curlEprime, curlE - p, curlE}]]

de[phi_, curlE_] := (2*e^2*n)/(3^(1/3)*
  Sqrt[2 Pi]*r^(2/3)*sigma^(4/3))*gSomething[phi, curlE]

phi = {.01, .02};
Quiet@Plot[de[#, curlE] & /@ phi, {curlE, -10, 10}, 
  PlotRange -> All, Evaluated -> True, PlotLegends -> ToString /@ phi]