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, erf is the error function and Ei is the exponential integral.

Other integrals

Definite integrals

Finally, a well known result, $${\displaystyle \int _{0}^{2\pi }e^{i(m-n)\phi }d\phi =2\pi \delta _{m,n}\qquad {\text{for }}m,n\in \mathbb {Z} }$$ where ${\displaystyle \delta _{m,n}}$ 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.