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 (the constant of integration) 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, erf is the error function and Ei is the exponential integral.

Other integrals

(Note that the value of the expression is independent of the value of n, which is why it does not appear in the integral.)

where

and Γ(x,y) is the upper incomplete gamma function.

The below formulae were proved by Toyesh Prakash Sharma (for ):[citation needed]

In 2023,Toyesh Prakash Sharma and Etisha Sharma found

Definite integrals

The last expression is the logarithmic mean. (the operator is the Double factorial) 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.

See also

References


Toyesh Prakash Sharma, Etisha Sharma, "Putting Forward Another Generalization Of The Class Of Exponential Integrals And Their Applications.," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.10, Issue.2, pp.1-8, 2023.[1]

Further reading