Let $f$ be a differentiable function such that it satisfies $\int_1^{xy} f(t)dt=x\int_1^{y} f(t)dt+y\int_1^{x} f(t)dt$ then find $f(e)$
Computing $f(x)$ if $\int_1^{xy} f(t) dt = y \int_1^x f(t) dt + x\int_1^y f(t) dt$ and $f(1) = 3$