`intsin^3(2x+1)\ dx`

Explanation

To solve the integral \( \int \sin^3(2x + 1) \, dx \), we can use substitution and trigonometric identities. Here’s a step-by-step solution:

### Step 1: Rewrite \( \sin^3(2x + 1) \)
We can express \( \sin^3(2x + 1) \) in terms of \( \sin^2(2x + 1) \):
\[ \sin^3(2x + 1) = \sin^2(2x + 1) \cdot \sin(2x + 1) \]
Using the identity \( \sin^2 \theta = 1 - \cos^2 \theta \), we have:
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