Choose the correct answers`int(cos2x)/((sinx+cosx)^2)dx`is equal(A) `(-1)/(sinx+cosx)+C` (B) `log|sinx+cosx|+C`C) `log|sinx-cosx|+C` (D) `1/((sinx+cosx)^2)`

Explanation

To solve the integral \( \int \frac{\cos(2x)}{(\sin x + \cos x)^2} \, dx \), we can follow these steps:

### Step 1: Rewrite \( \cos(2x) \)
We know that \( \cos(2x) \) can be expressed using the identity:
\[ \cos(2x) = \cos^2(x) - \sin^2(x) \]
Thus, we can rewrite the integral as:
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