On The Integral Invariant With Respect to a parameter

TL;DR

This paper investigates a class of integrals that are surprisingly easy to compute due to their parameter independence, but current symbolic tools struggle with them, prompting algorithm improvements.

Contribution

The paper identifies a class of parameter-independent integrals and proposes modifications to symbolic integration algorithms to compute them effectively.

Findings

Current symbolic tools fail on these integrals

Proposed algorithm modifications improve computation

Integrals are simpler than they appear

Abstract

Author presents a study of certain category of the integrals, which might look quite difficult to compute, but in fact are easily computable, because they do not depend on the parameter in the integrand. As simple and elementary the procedure is, the author discovered that the best of symbolic manipulation packages presently available fail quite miserably, when asked to compute these integrals. The author suggests proper modifications in the algorithms used for symbolic integration.