Elliptic Logarithm

A generalization of integrals of the form

$$\int_\infty^x {dt\over \sqrt{t^2+at}},$$

which can be expressed in terms of logarithmic and inverse trigonometric functions to

$${\rm eln}\,(x) \equiv \int_x^\infty {dt\over \sqrt{t^3+at^2+bt}}.$$

The inverse of the elliptic logarithm is the Elliptic Exponential Function.