1. Indefinite integral
    Integrals of polynomials  Integrals involving only exponential functions  Integrals involving exponential and trigonometric functions  Integrals involving the error function  Other integrals 

2. Definite integrals

3. See also

4. Further reading

5. External links

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 exponential and trigonometric functions

Integrals involving the error function

In the following formulas, {{math|erf}} is the error function and {{math|Ei}} is the exponential integral.

Other integrals

where

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

where

and {{math|Γ(x,y)}} is the gamma function.

when , , and

when , , and

Definite integrals

The last expression is the logarithmic mean.

(the Gaussian integral)

(see Integral of a Gaussian function)

(the operator is the Double factorial)

({{math|I₀}} is the modified Bessel function of the first kind)

See also

• Gradshteyn and Ryzhik

Further reading

• {{cite book |first=Victor Hugo |last=Moll |title=Special Integrals of Gradshteyn and Ryzhik: the Proofs – Volume I |volume=I |edition=1 |work=Series: Monographs and Research Notes in Mathematics |publisher=Chapman and Hall/CRC Press |date=2014-11-12 |isbn=978-1-48225-651-2 |url=http://www.crcpress.com/Special-Integrals-of-Gradshteyn-and-Ryzhik-the-Proofs---Volume-I/Moll/9781482256512 |access-date=2016-02-12}}
• {{cite book |first=Victor Hugo |last=Moll |title=Special Integrals of Gradshteyn and Ryzhik: the Proofs – Volume II |volume=II |edition=1 |work=Series: Monographs and Research Notes in Mathematics |publisher=Chapman and Hall/CRC Press |date=2015-10-27 |isbn=978-1-48225-653-6 |url=http://www.crcpress.com/Special-Integrals-of-Gradshteyn-and-Ryzhik-the-Proofs---Volume-II/Moll/9781482256536 |access-date=2016-02-12}}

External links

• Wolfram Mathematica Online Integrator
• {{cite web |first=Victor Hugo |last=Moll |title=List with the formulas and proofs in GR |url=http://www.math.tulane.edu/~vhm/Table.html |access-date=2016-02-12}}

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