`int_0^(pi/2) 1/(1+sinx)dx` equals `0` b. `1//2` c. `2` d. `3//2`

Explanation

To solve the integral \( I = \int_0^{\frac{\pi}{2}} \frac{1}{1 + \sin x} \, dx \), we can use a technique that involves multiplying the integrand by a suitable form of 1 to simplify the expression.

### Step 1: Multiply by Conjugate
We multiply the integrand by \( \frac{1 - \sin x}{1 - \sin x} \):

\[ I = \int_0^{\frac{\pi}{2}} \frac{1 - \sin x}{(1 + \sin x)(1 - \sin x)} \, dx \]
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