Evaluate the following integral: `int_0^(pi//2)1/(1+tanx)dx`

Explanation

To evaluate the integral \( I = \int_0^{\frac{\pi}{2}} \frac{1}{1 + \tan x} \, dx \), we can follow these steps:

### Step 1: Rewrite the Integral
We start by rewriting the integral using the identity \( \tan x = \frac{\sin x}{\cos x} \):
\[ I = \int_0^{\frac{\pi}{2}} \frac{1}{1 + \frac{\sin x}{\cos x}} \, dx = \int_0^{\frac{\pi}{2}} \frac{\cos x}{\cos x + \sin x} \, dx \]

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