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

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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