By using the properties of definite integrals, evaluate the integrals`int_0^(pi/2)(sin^(3/2)x dx)/(sin^(3/2)+cos^(3/2)x)`

Explanation

To evaluate the integral

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

we will use the property of definite integrals that states:

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