A calculus problem by Akshat Sharda

Calculus Level 3

\[\int^{1}_{0} \dfrac{x\tan^{-1}x}{(1+x^2)^{3/2}} \mathrm{d} x\]

If the answer to the above problem is \(\dfrac{1}{\sqrt{n}}-\dfrac{\pi}{4\sqrt{2}}\), then find the value of \(n\).

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