I am struggling to show that the improper integral $(\sin(1/x))^2$ from $1$ to infinity converges. After about half an hour of trying to integrate the function I looked on wolfram alpha and found the answer to include the sine integral.
This makes me doubt that evaluating the integral is the intended method to solve this function, as we have not studied the sine or cos integral. Also the question only asks if the integral converges, not to what value. So is there a different way I could show the integral converges, probably using the definition of a Riemann integral?
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