Integration! Can you do this?

Calculus Level 4

\[ \large I(a)=\displaystyle\int_{0}^{1} \frac{\tan^{-1}ax}{x\sqrt{1-x^{2}}} \, dx \]

If \(I(3)=\frac{π}{p}\ln(q+\sqrt{r})+s\) for integers \(p,q,r,s\), calculate \(p+q+r+s\).

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