# Over 3600 Years From Ahmes To ... ?

Calculus Level 5

The integral $\int_0^1 \frac{\tan^{-1}\sqrt{2+x^2}}{(1+x^2)\sqrt{2+x^2}}\,dx$ can be shown to be equal to $\frac{A\pi^B}{C}$ for positive integers $$A,B,C$$, where $$A,C$$ are coprime. What is the value of $$A+B+C$$?

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