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Question
(x3 + x2 + 1) sin x
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Solution
\[\text{ Let } u = x^3 + x^2 + 1; v = \sin x\]
\[\text{ Then }, u' = 3 x^2 + 2x; v' = \cos x\]
\[\text{ By product rule },\]
\[\frac{d}{dx}\left( uv \right) = uv' + vu'\]
\[\frac{d}{dx}\left[ \left( x^3 + x^2 + 1 \right) \sin x \right] = \left( x^3 + x^2 + 1 \right) \cos x + \left( 3 x^2 + 2x \right) \sin x \]
\[\]
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