I'm trying to find a way to unit test a numerical evaluation of:
\begin{align}
I(y) := \int\_{0}^{y} \frac{\sin(x)}{x} \frac{1}{\sqrt{1+ax}} \, \mathrm{d}x, \qquad a \in \mathbb{R}
\end{align}
Is there a nice representation of this function in terms of special functions? (Hopefully special functions that can be evaluated in Boost.Math, though any *other* representation not using numerical quadrature would be convenient.)

I should add that the limit $y\to \infty$, though aesthetically pleasing, is not the goal.