` x sin x`

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To solve the integral \( \int x \sin x \, dx \), we will use the method of integration by parts. Here are the steps: ### Step 1: Identify \( u \) and \( dv \) We choose: - \( u = x \) (which is algebraic) - \( dv = \sin x \, dx \) (which is trigonometric) ### Step 2: Differentiate \( u \) and Integrate \( dv \) ...
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