I know how to simulate a variable resistor in LTSpice. For example for a heating resistance the equation can be made by considering heating equation and can be expressed like R=(Ri-Ao*EXP(-time/To)) and further simulated,
If you open up the manual (
F1) and look under
LTspice > Circuit Elements > B, you'll see a table of functions, among which
sdt()) is the one you're looking for. For indefinite integration use simply
x can be the variable
time, and for definite integration you can use that in association with
idt(x-delay(x,1/T)), for example. The
time keyword has no meaning in
.AC analysis. Also see this.
One other way to integrate signals worth mentioning is to set the window time to the period that you want to integrate and then ctrl+click on the signal (can even be resistance) and it will give you and average and RMS value for the window time.