`int1/(1+cosx+sinx)\ dx=` `log|1+cotx/2|+C` (b) `log|1-tanx/2|+C` (c) `log|1-cotx/2|+C` (d) `log|1+tanx/2|+C`

Explanation

To solve the integral \(\int \frac{1}{1 + \cos x + \sin x} \, dx\), we will follow these steps:

### Step 1: Rewrite the Denominator
We start with the integral:
\[ I = \int \frac{1}{1 + \cos x + \sin x} \, dx \]
We can express \(\cos x\) and \(\sin x\) in terms of \(\tan \frac{x}{2}\). Using the identities:
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