Calculus · Medium problem

A chemical reactor's cumulative output is modeled by $V(x)=\displaystyle\int_1^{x^2}\sqrt{t+1}\,dt$ liters, where $x\ge0$ is the number of catalyst units added. At what value of $x$ is the instantaneous rate of change $V'(x)$ equal to $4\sqrt5$ liters per unit?