Integrator Circuit using Op-Amp Differentiator
No, it's not a good idea to drive the output of an op amp (which presents a low impedance to ground). The op amp would be fighting any circuit trying to drive its output -- an op amp will always try to drive its output to a certain value based on its inputs, but the output of the circuit that produces your \$V_{\text{in}}\$ would also try to drive the op amp's output to a likely different value. The circuit that would win the fight is the one that could drive more current. It's generally a bad idea to wire two analog outputs together.

If you need an integrator you can simply swap the resistor and capacitor with each other:



Source: The Integrator Amplifier