Calculus For All

Calculus Level 3

\[\large\ \int { \frac {x - 1}{(x + x\sqrt { x } + \sqrt { x }) \sqrt { \sqrt { x } ( x + 1) } } dx } = 4\tan ^{ -1 }{ \left( g( x) \right)} + C\]

If the above equation holds true for real-valued function \(g(x)\) and an arbitrary constant of integration \(C\), find the value of \(\left \lfloor g^{ 2 }(1) \right\rfloor \).

Notation: \(\lfloor \cdot \rfloor \) denotes the floor function.

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