Since you didn't post any code or errors, I don't know what was wrong. It was likely an error with your function definition. Functions that are going to be called with matrices need to be able to operate on matrices, so instead of using / we would use ./ which is elementwise division (otherwise we would be attempting matrix divison, which is not defined).
Here's my solution:
f = @(x) (exp(x) - 1)./x
sol = integral(f,1*10^-19,Inf)
I can't tell exactly what function you are trying to integrate, so I apologize if it is the incorrect one.