Turn off convergence checking - "formal" integration

edit

Apologies if something like this has been posted already - I have not found it.

I would like to be able to compute "formal integrals" of functions f(t,x) with respect to x, without having to use assume() to put restrictions on x. In particular, I want to compute integral(e^(-t)*f,t,0,infinity). For example, right now if I try

integrate(e^(-t)*e^(x*t),t,0,infinity)

I need to assume(x < 1) for it to work. This is fine for simple integrals, but if the function f is more complicated, using assume() becomes annoying. I'd like to be able to use a formal integral so that integrate(e^(-t)*e^(t*f),t,0,infinity) returns 1/(1 - f) whenever f is a function only of x, without needing to use assume() - or an equivalent function.

Thanks!

Edit: It occurred to me that just using integrate(f,t).subs(t=0) seems to work some of the time. I'd still like a better way, though