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.

Indefinite integral

Indefinite integrals are antiderivative functions. A constant may be added to the right hand side of any of these formulas, but has been suppressed here in the interest of brevity.

Integrals of polynomials

  • Integrals involving only exponential functions

  • Integrals involving the error function

In the following formulas, is the error function and is the exponential integral.

  • Other integrals

  • where


where


and is the upper incomplete gamma function.


  • when,, and
  • when,, and

  • Definite integrals

The last expression is the logarithmic mean.



where is the Polylogarithm.


where is the Euler–Mascheroni constant which equals the value of a number of definite integrals.


Finally, a well known result,
where is the Kronecker delta.