Evaluate the following integral:`int_0^(pi//2)(tan^7x)/(tan^7x+cot^7x)dx`

Explanation

To evaluate the integral

\[ I = \int_0^{\frac{\pi}{2}} \frac{\tan^7 x}{\tan^7 x + \cot^7 x} \, dx, \]

we can use a property of definite integrals. Specifically, we can use the substitution \( x = \frac{\pi}{2} - t \).

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