Answer
$$\int_{0}^{1} \int_{0}^{x} \int_{0}^{x y} x d z d y d x=\frac{1}{10}$$
Work Step by Step
\begin{align}
I&=\int_{0}^{1} \int_{0}^{x} \int_{0}^{x y} x d z d y d x\\
&=\int_{0}^{1} \int_{0}^{x}[x z]_{0}^{x y} d y d x\\
&=\int_{0}^{1} \int_{0}^{x} x^{2} y d y d x\\
&=\int_{0}^{1}\left[\frac{x^{2} y^{2}}{2}\right]_{0}^{x} d x\\
&=\int_{0}^{1} \frac{x^{4}}{2} d x\\
&=\left[\frac{x^{5}}{10}\right]_{0}^{1}\\
&=\frac{1}{10}
\end{align}
