Exponential Integral Calculator

Calculate the exponential integral of a number x, which is defined as Ex(1) = ∫1∞ e-t/t dt for real x > 0.

Input Parameters

Calculation Results

Calculation Formula

Ex(1) = ∫1∞ e-t/t dt

Where:
Ex(1) = Exponential Integral
x = Real number input

Result:

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Exponential Integral Calculator Calculator Usage Guide

Learn how to use the Exponential Integral Calculator and understand its mathematical properties

What is the Exponential Integral?

The exponential integral Ex(1) is a special function that arises in mathematics, physics, and engineering. It is defined as:

Ex(1) = ∫1∞ e-t/t dt

This calculator specifically calculates Ex(1) where the parameter x is the input value.

How to Use This Calculator

  1. Enter a positive real number for x in the input field.
  2. Click the "Calculate" button to compute the exponential integral.
  3. The result will be displayed with high precision.
  4. Click "Reset" to clear all inputs and results.

Mathematical Properties

The exponential integral has several important properties:

  • For large x values, Ex(1) ≈ e-x/(x)
  • For small x values (x near 0), Ex(1) ≈ 1 + x + x²/2 + x³/3! + ...
  • The function is only defined for x > 0.

Applications

The exponential integral appears in various fields including:

  • Quantum physics and quantum chemistry
  • Probability theory and statistics
  • Heat and mass transfer problems
  • Financial mathematics