Numerical integration of symbolic equation

I am trying to numerical integrate the function with respect to x. I am not able to solve it. Can anyone help me?

fun = @(x) (1./(exp(0.014342./(x*t))-1).*1./x.^4);

q = integral(@(x) fun(x), 0, x1)

Note: t is a unknown constant over here and limits are from 0 to x1.

Answer 1

[Walter Roberson]

This is impossible to do as a numeric integration.

[Walter Roberson]

The equation being integrated is fundamentally discontinuous at t=0 and at x=0

[Walter Roberson]

If you write the function as

syms x x0 t A real
assume(x0>=0 & t>0 & A>0 & x>=0)
fun = @(x) (1./(exp(A/(x*t))-1)./x.^4);
Q = int(fun(x), x, 0, x0)

Then MATLAB still cannot handle it... but pop it over into Maple and Maple can handle that, returning

%Maple notation. Beware the ln and Pi and I:
1/3*(6*t^3*polylog(3,exp(A/x0/t))*x0^3-A*t^2*x0^2*Pi^2+6*A*t^2*x0^2*dilog(exp(A/x0/t))+3*A^2*t*x0*ln(-1+exp(A/x0/t))+3*I*A^2*t*x0*Pi+A^3)/A^3/x0^3

In MATLAB notation, for A = 0.014342

@(t,x0)1.0./x0.^3.*(x0.^2.*(t.^2.*dilog(exp(1.4342e-2./(t.*x0))).*9.72323000800358e+3-t.^2.*1.599407227996604e+4)+x0.*(t.*2.190484349177098e+2i+t.*log(exp(1.4342e-2./(t.*x0))-1.0).*6.972528238739367e+1)+3.333333333333333e-1)+t.^3.*polylog(3,exp(1.4342e-2./(t.*x0))).*6.779549580256296e+5