Why is it that we use capacitors in Differentiator & Integrator circuits (comprising Op Amps) & not inductors?
A lot of circuits require medium/high impedance values for even moderately low frequencies such as audio and a capacitor of say 10 nF at 1 kHz has an impedance of 15.9 kOhm. An inductor having this impedance at 1 kHz would have a value of 2.53 henries.

Now that isn't a small value to fit in a space for a surface mount component. That's one reason and the next is cost - try finding a 2.5 henry coil in farnell, digikey or mouser and see how much change you have out of a dollar or a pound. The 10nF will cost you about a couple of pennies maximum.

So, it's not small and it's not cheap and a side effect of it not being small is that it will possess significant parasitic capacitance (several pico farads if not more) and this makes it less than perfect. I'm certainly not saying caps are perfect but they are a couple of orders of magnitude more perfect than an inductor.

Also it will have a significant DC resistance as it is made as small as it can be. It won't be good at handling currents like capacitor is and the core will probably saturate.

Bad idea - use capacitors.