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Wikipedia / 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 (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, is the error function and 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.)
 a_{mn}=\begin{cases}1   &\text{if } n = 0, \\ \\ \dfrac{1}{n!} &\text{if } m=1, \\ \\ \dfrac{1}{n}\sum_{j=1}^{n}ja_{m,n-j}a_{m-1,j-1}  &\text{otherwise} \end{cases}
 and Γ(x,y) is the Incomplete gamma function#Definitionupper incomplete gamma function.

Definite integrals

The last expression is the logarithmic mean.

 !! is the Double factorialDouble factorial)
 \operatorname{Li}_{s}(z) is the Polylogarithm#Integral representationsPolylogarithm.
 \gamma is the Euler–Mascheroni constant#IntegralsEuler–Mascheroni constant which equals the value of a number of definite integrals.

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.https://www.isroset.org/pdf_paper_view.php?paper_id=3100&1-ISROSET-IJSRMSS-08692.pdf

Further reading

  • Toyesh Prakash Sharma, https://www.isroset.org/pdf_paper_view.php?paper_id=2214&7-ISROSET-IJSRMSS-05130.pdf