\( f(x)=
\begin{cases}
\frac{\sin^3(\sqrt{3}) \cdot \log(1+3x)}{(\tan^{-1}\sqrt{x})^2 (e^{5\sqrt{x}}-1)x}, & x\neq 0 \\
a, & x=0
\end{cases}
\)
is continuous in \( [0,1] \), then \( a \) equals to
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For continuity at 0, always use standard approximations like $\log(1+x)\approx x$.