`intsin^2(2x+5)\ dx`

Explanation

To solve the integral \( \int \sin^2(2x + 5) \, dx \), we can use the trigonometric identity for sine squared. Here’s a step-by-step solution:

### Step 1: Use the identity for sine squared
We know that:
\[ \sin^2 \theta = \frac{1 - \cos(2\theta)}{2} \]
In our case, let \( \theta = 2x + 5 \). Thus,
...