The following is a list of integrals of exponential functions. For a complete list of integral functions, please see the list of integrals.

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.

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

where ${\displaystyle c_{2j}={\frac {1\cdot 3\cdot 5\cdots (2j-1)}{2^{j+1}}}={\frac {(2j)!}{j!2^{2j+1}}}\ .}$

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

where ${\displaystyle a_{mn}={\begin{cases}1&{\text{if }}n=0,\\\\{\dfrac {1}{n!}}&{\text{if }}m=1,\\\\{\dfrac {1}{n}}\sum _{j=1}^{n}ja_{m,n-j}a_{m-1,j-1}&{\text{otherwise}}\end{cases}}}$

and Γ(x,y) is the upper incomplete gamma function.

The last expression is the logarithmic mean.