$ \int f(x) \sin x \cos x \, dx = \frac{1}{2} (b^2 - a^2) \log f(x) + c $, where $ c $ is the constant of integration. Then, $ f(x) = \ldots $

Question

$ \frac{2}{ab \sin 2x} $

$ \frac{2}{(b^2 - a^2) \sin 2x} $

$ \frac{2}{ab \cos 2x} $

$ \frac{2}{(b^2 - a^2) \cos 2x} $

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