List of integrals of exponential functions

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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[edit]

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[edit]

Integrals involving only exponential functions[edit]

Integrals involving exponential and trigonometric functions[edit]

Integrals involving the error function[edit]

In the following formulas, erf is the error function and Ei is the exponential integral.

Other integrals[edit]

(Note that the value of the expression is independent of the value of n, which is why it does not appear in the integral.)
and Γ(x,y) is the gamma function.
when , , and
when , , and

Definite integrals[edit]

The last expression is the logarithmic mean.

(the Gaussian integral)
(see Integral of a Gaussian function)
(!! is the double factorial)
(I0 is the modified Bessel function of the first kind)

See also[edit]

Further reading[edit]

External links[edit]