Integral

Calculus Level pending

\[\int \frac{f'(x)g(x) - g'(x)f(x)}{(f(x) + g(x))\sqrt{f(x)g(x) - g^{2}(x)}} dx = \sqrt{m} tan^{-1} \left(\sqrt{\frac{f(x) - g(x)}{n g(x)}}\right) + C \]

Where \( m, n \in \mathbb N \), 'C' is constant of integration and \( g(x) > 0\)

Then find

\(m^{2} + n^{2}\)

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