Solving ODE that contains an integral

I'm trying to solve the above differential equation using ODE15i where C1-C4 and V0 are some known constants. My issue comes in how to handle the fourth term containing the integral. My thought process right now is to declare global dummy vectors for t and dV/dt, update them each time the residual function is called, and use them to determine the value of the integral using the trapz function. Any insights on if this method would work or if there's a better way to go about it would be greatly appreciated, thanks!