Can you please help me to prove the integrals \begin{equation*} \int_0^\pi \frac{x}{\sin(x)}~\text{and}~\int_0^\infty \frac{1}{\sqrt{x}}\cos(x^{-1}) \end{equation*} are divergent? Please I really need it.
Thank you.
2026-04-02 20:53:19.1775163199
How can I prove that these integrals do not converge?
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