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For the benchmark p-integral with $p>0$, $\int_1^\infty x^{-p}\,dx$ converges when $p>1$ and diverges when $0<p\le1$. The case $p=2$ provides a convenient convergent upper bound for comparison tests.

Conditions: The exponent $p$ is a positive real number ($p>0$).; The integral is evaluated from $1$ to $\infty$.

For the benchmark p-integral with $p>0$, $\int_1^\infty x^{-p}\,dx$ converges when $p>1$ and diverges when $0<p\le1$. The case $p=2$ provides a convenient convergent upper bound for comparison tests.

Conditions: The exponent $p$ is a positive real number ($p>0$).; The integral is evaluated from $1$ to $\infty$.