Integral of repeated convolution of the unit step function

Integral of repeated convolution of the unit step function

Background
Let $\theta$ be the unit step function: $$\theta(x) = \begin{array}{ll}
\left\{ \begin{array}{ll} 0 & x \lt 0 \\ 1 & x\ge 0. \end{array}\right.
\end{array} $$ Further, the convolution of two functions $f$ and $g$ is
the function: $$ (f \star g)(x) = \int_{-\infty}^{\infty} f(x-y)g(y) dy.
$$ Let $\theta^{\star n}(x)$ denote the repated convolution (and not
pointwise multiplication) of the unit step function.
Question
I know that, by simple integration, $$ \theta^{\star n}(x) = \theta(x)
\frac{x^{n-1}}{(n-1)!} $$ but I am unable to follow how this integral was
calculated (the detailed calculations were not provided, just this
result). Can anybody give me a hint? Thank you.