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.

  • $\begingroup$ 2) need other brackets .. $\endgroup$ – Mohamed Nov 25 '13 at 1:42


  • the first : When $x \to \pi$, we have $\sin x = \sin (\pi -x) \sim \pi - x$ and $\int_1^{\pi} \frac{\pi}{\pi -x}$ diverges.

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