MathNet 2005 — Part 01 Question 17

Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be a continuous function with $\int_{0}^{1} f(x) f^{\prime}(x) d x=0$ and $\int_{0}^{1} f(x)^{2} f^{\prime}(x) d x=18$. What is $\int_{0}^{1} f(x)^{4} f^{\prime}(x) d x$?