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
Definite integrals
Finally, a well known result,
∫ 0 2 π e i ( m − n ) ϕ d ϕ = 2 π δ m , n for m , n ∈ Z {\displaystyle \int _{0}^{2\pi }e^{i(m-n)\phi }d\phi =2\pi \delta _{m,n}\qquad {\text{for }}m,n\in \mathbb {Z} }
where δ m , n {\displaystyle \delta _{m,n}} is the Kronecker delta.
See also Gradshteyn and Ryzhik
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 Moll, Victor Hugo (2014-11-12). Special Integrals of Gradshteyn and Ryzhik: the Proofs – Volume I. Vol. I (1 ed.). Chapman and Hall/CRC Press. ISBN 978-1-48225-651-2. Retrieved 2016-02-12. {{cite book}}: |work= ignored (help) Moll, Victor Hugo (2015-10-27). Special Integrals of Gradshteyn and Ryzhik: the Proofs – Volume II. Vol. II (1 ed.). Chapman and Hall/CRC Press. ISBN 978-1-48225-653-6. Retrieved 2016-02-12. {{cite book}}: |work= ignored (help) Toyesh Prakash Sharma, https://www.isroset.org/pdf_paper_view.php?paper_id=2214&7-ISROSET-IJSRMSS-05130.pdf
External links Wolfram Mathematica Online Integrator Moll, Victor Hugo. "List with the formulas and proofs in GR". Retrieved 2016-02-12.