I am unsure if this integral is convergent or not based on the $p$ rule that if $P$ is greater than one, it is convergent? $$\int_\pi^\infty\frac{1+\sin(x)}{x^2} \; dx$$ and since $1+\sin(x)$ is always positive, it can be replaced with any integer greater or equal to one?
2026-05-06 03:08:19.1778036899
Convergence with p integral
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One may observe that $$0\leq\int_\pi^\infty\frac{1+\sin(x)}{x^2} \; dx\leq\int_\pi^\infty\frac{2}{x^2} \; dx=\frac{2}{\pi }$$