Module risch 

Risch algorithm for symbolic integration

Basic implementation covering:

• Simple exponential and logarithmic functions
• Rational function integration via Hermite reduction
• Non-elementary detection
• Completeness guarantee for basic cases

The Risch algorithm is a decision procedure that either:

1. Computes the elementary antiderivative
2. Proves no elementary antiderivative exists

This implementation handles exponential extensions (e^x, e^(ax)), logarithmic extensions (ln(x), 1/x patterns), and rational functions in their basic forms.

Modules

differential_extension

Differential extension tower construction

helpers

Helper functions for Risch algorithm

hermite

Hermite reduction for separating polynomial and rational parts

rational

Rational function integration using Hermite reduction algorithm

rde

Risch Differential Equation (RDE) solving

Enums

RischResult

Risch integration result

Functions

try_risch_integration

Main Risch integration entry point