Question 44
Find all integrable functions $f : [0, 1] \to \mathbb{R}$ with the property: for every $x \in [0, 1]$,
$$
\int_0^x f(t) dt = (f(x))^{2015} + f(x).
$$
$$
\int_0^x f(t) dt = (f(x))^{2015} + f(x).
$$
MathNet 2015-part-05 — 191 problems (EN–VI) Question 44
Math Olympiad Vault · MathNet 2015-part-05 — 191 problems (EN–VI)