For a constant input voltage the voltage across the feedback C would rise linearly, however, since the input voltage drops, there will be an increase of the output voltage following an exponential function.
Sorry, I did not express myself clear enough. "Following an exponential function" means, of course, following the function (1-exp) . That means - similarly to charging a cap through a resistor - the voltage across the feedback capacitor (identical to the output voltage of the OTA) reaches a final value which depends only on the input voltage as well as the cap ratio.