A problem from G.H. hardy`s book

Calculus Level 5

If the antiderivative, \(\displaystyle \int \dfrac{dx}{1+x^4} \) is in the form

\[ \dfrac1{a\sqrt b} \left [\ln\left(\dfrac{1+x \sqrt b + x^2}{1-x\sqrt b + x^2} \right) + 2\tan^{-1} \left(\dfrac{x\sqrt b}{1-x^2} \right) \right ] \]

find \(a\times b\).

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