A calculus problem by Tunk-Fey Ariawan

Calculus Level 5

01ln(x42x2+5)ln(5x42x2+1)1x2dx {\int_0^1\frac{\ln\left(x^4-2x^2+5\right)-\ln\left(5x^4-2x^2+1\right)}{1-x^2}\, dx}

Given that the integral above is equal to παarctanβγδ \pi^\alpha\arctan\sqrt{\dfrac{\sqrt{\beta}-\gamma}{\delta}} , where α,β,γ,δ\alpha, \beta, \gamma, \delta are integers with β\beta square-free.

Calculate α+β+γ+δ{\alpha+\beta+\gamma+\delta}.

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