Find the value of `int_(-2)^(2)(sin^(-1)(sinx)+cos^(-1)(cosx))/((1+x^(2))(1+[(x^(2))/5]))dx`, where [.] represents the greatest integer function.

Explanation

To solve the integral

\[ I = \int_{-2}^{2} \frac{\sin^{-1}(\sin x) + \cos^{-1}(\cos x)}{(1 + x^2)\left(1 + \left\lfloor \frac{x^2}{5} \right\rfloor\right)} \, dx, \]

we can follow these steps:

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