I am not able to find the following definition: When an integral is said to be logarithmically divergent integral? Can someone help me to get it?
2026-04-07 21:09:14.1775596154
Logarithmically divergent integrals
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For an integral to be logarithmic divergent, conditions are met for integrals of the type $$ I(x) = \int_{x_0}^x \frac{1}{p}\mathrm d p $$ or potenitally of the form $$I(x) = \int_{x_0}^x \frac{1}{p}f(p)\mathrm d p$$ where $f(p)$ approaches a finite limit when $p \to\infty$). In both of these cases, the integral diverges to infinity when $x\to\infty$, and is observede to do so slowly.
(I deliberately chose the free parameter $p$ here as I am assuming you are a student of some kind of QFT as this notion of divergence appears in Perturbative QFT?)