`int_0^(pi//2)1/(1+cot^3x)dx` is equal to `0` b. `1` c. `pi//2` d. `pi//4`

Explanation

To solve the integral \( I = \int_0^{\frac{\pi}{2}} \frac{1}{1 + \cot^3 x} \, dx \), we can use the property of definite integrals which states that:

\[ \int_a^b f(x) \, dx = \int_a^b f(a + b - x) \, dx \]

In our case, \( a = 0 \) and \( b = \frac{\pi}{2} \). Therefore, we can rewrite the integral as follows:

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