Word Count : 288

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To evaluate the integral: \[ \int_{0}^{1} \left( 2x \sin\left( \frac{1}{x} \right) - \cos\left( \frac{1}{x} \right) \right) \, dx \] we can apply the Fundamental Theorem of Calculus. This involves recognizing the antiderivatives of the components and evaluating them at the limits of integration. ### Step 1: Separate the integral into two parts: \[ \int_{0}^{1} \left( 2x \sin\left( \frac{1}{x} \right) \right) \, dx - \int_{0}^{1} \cos\left( \frac{1}{x} \right) \, dx \] ### Step _____ __________ _____ _______ ____.
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