A calculus problem by Tunk-Fey Ariawan

Calculus Level 5

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

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.