Evaluate `int(1)/(1+sinx)dx`.

Explanation

To evaluate the integral \(\int \frac{1}{1 + \sin x} \, dx\), we can use a technique called rationalization. Here’s the step-by-step solution:

### Step 1: Rationalize the Denominator
We start by multiplying the integrand by \(\frac{1 - \sin x}{1 - \sin x}\):
\[ \int \frac{1}{1 + \sin x} \, dx = \int \frac{1 - \sin x}{(1 + \sin x)(1 - \sin x)} \, dx \]

...