Integration! Can you do this?

Calculus Level 5

I(a)=01tan1axx1x2dx \large I(a)=\displaystyle\int_{0}^{1} \frac{\tan^{-1}ax}{x\sqrt{1-x^{2}}} \, dx

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

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