%The format of the equations should be correct. Af for plotting and evaluating the integral, I am not correct (I didn't get it to work) but hopefully this is a start. If you have questions about integrating within Matlab, type "help integrate" into the command window. (Also try "help fplot" etc).
Check out the attached document for more info on function handles.
%Define constants (for example)
del=2; delta = 3; alpha=4; L=5; q_c = 10;
%Create the function inside the integral:
f =@(q) q.^del.*coth(q)/((del+q.^del.*L.^del)/(del.*alpha)).^(del+alpha)
f_integral = integral(f,0,q_c)
%The Left Hand Side (LHS) vs RHS:
%F = E/E_0
F = del+delta.^del.*L.^del.*f_integral %RHS
Let me know if this helps.
