Evaluate: `int_(-pi/2)^(pi/2)log{(a x^2+b x+c)/(a x^2-b x+c)(a+b)|sinx|}dx`

Explanation

To evaluate the integral

\[ I = \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \log\left(\frac{a x^2 + b x + c}{(a x^2 - b x + c)(a + b) |\sin x|}\right) dx, \]

we can break it down into simpler parts using properties of logarithms and symmetry.

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