Definite Integral of an Exponential Function Now that we know how to get an antiderivative (or indefinite inte-gral) of an exponential function we can consider definite integrals.

List of integrals of exponential functions The following is a list of integrals of exponential functions. For a complete list of Integral functions, please see the list of integrals.

The integral will definitely not be infinite: it falls off equally fast in both positive and negative directions, and in the positive direction for x greater than 1, it’s smaller than e-ax, which we know converges.

Application to the cosine integral Consider the integrals corresponding to (1) with e−t replaced by cos t:

Rule: Integrals of Exponential Functions Exponential functions can be integrated using the following formulas. ∫ exdx = ∫ axdx = ex + C

To integrate other trigonometric functions, you can convert them to sine and cosine functions and use the formulas above. We summarize the formulas for integration of functions in the table below and …

Dec 10, 2025 · Exponential and logarithmic functions arise in many real-world applications, especially those involving growth and decay. Substitution is often used to evaluate integrals involving …

5.8 Numerical Integration Chapter 6: Exponentials and Logarithms (PDF) 6.1 An Overview 6.2 The Exponential e x 6.3 Growth and Decay in Science and Economics 6.4 Logarithms 6.5 Separable …

Applications of exponential integrals include number theory, quantum field theory, Gibbs phenomena, and solu-tions of Laplace equations in semiconductor physics.

This document provides a list of integrals of exponential functions. It includes indefinite integrals, which are antiderivatives with the constant of integration suppressed for brevity.