Evaluate the following integrals: `int_0^(pi//4)(sin^2xcos^2x)/((sin^3x+cos^3x)^2)dx`

Explanation

To evaluate the integral

\[ I = \int_0^{\frac{\pi}{4}} \frac{\sin^2 x \cos^2 x}{(\sin^3 x + \cos^3 x)^2} \, dx, \]

we can follow these steps:

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