A calculus problem by Tunk-Fey Ariawan

Calculus

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

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

Calculate ${\alpha+\beta+\gamma+\delta}$ .