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We are asked to evaluate: [ \int_{0}^{1} \left( 2x \sin \frac{1}{x} - \cos \frac{1}{x} \right) dx ] using the Fundamental Theorem of Calculus. Notice that the derivative of (\sin \frac{1}{x}) is: [ \frac{d}{dx} \left( \sin \frac{1}{x} \right) = \cos \frac{1}{x} \cdot \frac{d}{dx} \left( \frac{1}{x} \right) = \cos \frac{1}{x} \cdot _______ ____ ___ ____ ______ ____ __________ _____.
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