Integrate ∫ cos(1/x)/x^2 dx: Steps & Solutions

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The discussion focuses on solving the integral ∫ (cos(1/x) / x^2) dx, with participants encouraged to share their steps for collaborative learning. A suggestion is made to use substitution as a method to simplify the problem, emphasizing the need to identify an appropriate substitution and its derivative. The community expresses a welcoming attitude, inviting users to engage and learn rather than simply providing answers. Overall, the thread promotes a collaborative approach to solving complex integrals. Engaging in this manner fosters a deeper understanding of integration techniques.
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∫ (cos (1/x) / x^2 dx (Please show steps.)
 
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You show us *your* steps, and then we can offer tutorial help. We do not do your work for you here on the PF.
 
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\int \frac{cos \frac{1}{x}}{x^2} dx
Why couldn't you try the method of substitution? Find an appropriate substitution, and then you need to find something that can serve as du or rather, something that can simplify the denominator.

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