How can take an integral for a dependent expression?

I am trying to take the integral of an expression and am running into trouble on how to do it symbolically. I have used the trapz method and it works, however in following work this method seems to be inadequate. I have included my script for reference, ultimately I want to take the integrals denoted as Qsfun and Qcfun which are dependent on the variables xg and Vg. Thanks in advance for any insight and help.

Script

Vg = linspace(1.5e-1, 5, 3000);%Energy gap defined by us, allows optimization of where the cell has the highest efficiency.
for t = 1:length(Vg)

xg(t) = (q*Vg(t)) /(k*Ts); %Xg value operating on the energy gap value and dependent on the temp of the sun.
xgc(t) = (q*Vg(t)) /(k*Tc); %Xg value operating on the energy gap value and dependent on the temp of the cell.

x = linspace(xg(t),1000, 10000);%Size iteration of x based on values xg(t) to 1000, with 10000 interval points
for l = 1:length(x);

Qsfun(l) =(x(l)^2)/(exp(x(l))-1);
end
a = linspace(xgc(t),30*xgc(t), 30000);%Size iteration of a based on values xgc(t) to 30*xgc, with 30000 interval points
for y = 1:length(a);

Qcfun(y) =(a(y)^2)/(exp(a(y))-1);
end
Intqs(t) = trapz(x,Qsfun);
Intqc(t) = trapz(a,Qcfun);
%Iqs(t) = xg*trapz(x,Qsfun);
%Iqc(t) = xg*trapz(x,Qcfun);

%The number of quanta of frequency greater than vg incident per unit area time
Qs(t) = ((2*pi*((k*Ts)^3))/((h^3)*(c^2)))*Intqs(t);
Qc(t) = ((2*pi*((k*Tc)^3))/((h^3)*(c^2)))*Intqc(t); 

b = linspace(1e-10, 100, 3000);

for mm = 1:length(b)
Psfun(mm) = (b(mm)^3)/(exp(b(mm))-1); %Function of Plancks distribution integral
end

IntPs = trapz(b,Psfun);

u(t) = (xg(t)*Intqs(t))/IntPs;
end

Answer 1

[Torsten]

I get

2*x*Polylog(2,exp(x))-2*Polylog(3,exp(x))-x^3/3+x^2*log(1-exp(x))

for the integral of

x^2/(exp(x)-1)

Take a look at

http://de.mathworks.com/help/symbolic/polylog.html

for more information about the polylogarithm.

Best wishes

Torsten.

[Jarett]

Torsten, Your answer was not exactly what I was looking for. I am wanting to know what the code should be in order to integrate the Qcfun and Qsfun. I am using this integral to then multiply by the constant denoted in Qs(t) and Qc(t). Ultimately the integral will be changing values for every value of Vg as xg is dependent on Vg and the integral limits should be from xg or xgc respectively to infinity. Hopefully this clarifies. I have used the trapz method as shown in my script and get a working function, however in later parts of my problem the trapz method doesnt seem to be accurate enough, thus I would like to integrate the function more symbolically such as Qsfun = @(x)(x^2/e^x -1).

[Torsten]

If you don't like the analytical expression for your integral, maybe

http://de.mathworks.com/help/matlab/ref/quadgk.html

is of help.

Best wishes

Torsten.

[Jarett]

Torsten,

Thanks for the advice. Solved my issue, simply was missing a period to compute element wise. Thanks for the attention though.

-Jarett