From 0 to 1

Calculus Level 3

If the definite integral \(x^{2}\) \(tan^{-1} x \) with respect to \(x\) from \(0\) to \(1\) can be expressed as \(\frac{\pi}{p}\) - \(\frac{q}{r}\) + \(\frac{ln s}{t} \) where gcd (q, r) = 1 and p, q, r, s and t are all positive integers, \(p + q +r +s + t =?\)

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