Example 3: Integral of the entire real line

The integral \int_{-\infty}^\infty \frac{x} {4e^x + 9e^{-x}} \, dx is computed and compared to its expected value. This integral is evaluated in Gradshteyn and Ryzhik (equation 3.417.1).
using System;
using Imsl.Math;

public class QuadratureEx3 : Quadrature.IFunction
{
	public double F(double x)
	{
		return x / (4.0 * Math.Exp(x) + 9.0 * Math.Exp(-x));
	}


	public static void  Main(String[] args)
	{		
		Quadrature q = new Quadrature();
		Quadrature.IFunction fcn = new QuadratureEx3();
		double result = q.Eval(fcn, Double.NegativeInfinity, 
			Double.PositiveInfinity);
		
		double expect = System.Math.PI * System.Math.Log(1.5) / 12.0;
		Console.Out.WriteLine("result = " + result);
		Console.Out.WriteLine("expect = " + expect);
	}
}

Output

result = 0.106150517076628
expect = 0.106150517076633

Link to C# source.

Reference

Gradshteyn, I. S. and I. M. Ryzhik (1965), Table of Integrals, Series, and Products , Academic Press, New York.