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.