Leaky integrator from Switched capacitor integrator?
Here's a simple method:

Add a capacitor, \$C_{leak}\$, to your circuit. One terminal is always grounded. The other terminal is connected either to the op-amp's output or to its inverting terminal, alternating between the two at the switching frequency \$f_S\$. This capacitor acts like a resistor of value \$R_{eq}=1/(f_SC_{leak})\$ between the op-amp's output and its inverting terminal.