Module integration 

Symbolic integration module for computing indefinite integrals.

This module provides functionality for computing antiderivatives of mathematical expressions using standard integration techniques including:

• Power rule
• Sum and difference rules
• Constant multiple rule
• Standard integrals table (trigonometric, exponential, logarithmic)

Example

use thales::integration::{integrate, IntegrationError};
use thales::ast::{Expression, Variable};

// Integrate x^2 with respect to x
let x = Expression::Variable(Variable::new("x"));
let x_squared = Expression::Power(Box::new(x.clone()), Box::new(Expression::Integer(2)));

let result = integrate(&x_squared, "x").unwrap();
// Result: x^3/3 + C (constant of integration handled separately)

Enums

IntegrationError

Error types that can occur during integration.

Functions

definite_integral

Compute the definite integral of an expression over [lower, upper].

definite_integral_with_fallback

Compute definite integral with numerical fallback.

definite_integral_with_steps

Compute definite integral with step-by-step explanation.

improper_integral_to_infinity

Evaluate improper integral ∫_a^∞ f(x) dx using limit.

integrate

Compute the indefinite integral of an expression with respect to a variable.

integrate_by_parts

Attempt to integrate using integration by parts: ∫u dv = uv - ∫v du

integrate_by_parts_with_steps

Integration by parts with detailed steps.

integrate_by_substitution

Attempt to integrate using u-substitution.

integrate_with_substitution

Public function for u-substitution with step tracking.

numerical_integrate

Numerical integration using adaptive Simpson’s rule.

tabular_integration

Tabular method for integration by parts.

Type Aliases

IntegrationResult

Result type for integration operations.