The following is a list of integral

Integral

Integration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus...

s of exponential function

Exponential function

In mathematics, the exponential function is the function ex, where e is the number such that the function ex is its own derivative. The exponential function is used to model a relationship in which a constant change in the independent variable gives the same proportional change In mathematics,...

s. For a complete list of Integral functions, please see the list of integrals.

Indefinite integrals

Indefinite integrals are antiderivative

Antiderivative

In calculus, an "anti-derivative", antiderivative, primitive integral or indefinite integralof a function f is a function F whose derivative is equal to f, i.e., F ′ = f...

 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.

for

( is the Error function

Error function

In mathematics, the error function is a special function of sigmoid shape which occurs in probability, statistics and partial differential equations...

)

where

where

and is the Gamma Function

Gamma function

In mathematics, the gamma function is an extension of the factorial function, with its argument shifted down by 1, to real and complex numbers...

when , , and
when , , and

Definite integrals

for , which is the logarithmic mean

Logarithmic mean

In mathematics, the logarithmic mean is a function of two non-negative numbers which is equal to their difference divided by the logarithm of their quotient...

(the Gaussian integral

Gaussian integral

The Gaussian integral, also known as the Euler-Poisson integral or Poisson integral, is the integral of the Gaussian function e−x2 over the entire real line.It is named after the German mathematician and...

)

(see Integral of a Gaussian function)


(!! is the double factorial)





( is the modified Bessel function

Bessel function

In mathematics, Bessel functions, first defined by the mathematician Daniel Bernoulli and generalized by Friedrich Bessel, are canonical solutions y of Bessel's differential equation:...

of the first kind)

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