Evaluate : `int " sin 5x . cos x dx "`

Explanation

To evaluate the integral \( \int \sin(5x) \cos(x) \, dx \), we can use a trigonometric identity and integration techniques. Here’s the step-by-step solution:

### Step 1: Use the Trigonometric Identity
We can use the identity:
\[ 2 \sin(a) \cos(b) = \sin(a + b) + \sin(a - b) \]
In our case, let \( a = 5x \) and \( b = x \). Thus, we can rewrite:
...