Let f be a differentiable function in the interval (0, ∞) such that f(1)=1 and lim_t → x (t^2 f(x)-x^2 f(t))/(t-x)=1 for each x>0. Then 2 f(2)+3 f(3)…

Let $\displaystyle f$ be a differentiable function in the interval $\displaystyle (0, \infty)$ such that $\displaystyle f(1)=1$ and $\displaystyle \lim _{t \rightarrow x} \frac{t^2 f(x)-x^2 f(t)}{t-x}=1$ for each $\displaystyle x>0$. Then $\displaystyle 2 f(2)+3 f(3)$ is equal to $\displaystyle \_\_\_\_$.