The following is a list of integrals (antiderivative functions) of logarithmic functions. For a complete list of integral functions, see list of integrals.
Note: x > 0 is assumed throughout this article, and the constant of integration is omitted for simplicity.
n consecutive integrations
For
consecutive integrations, the formula
![{\displaystyle \int \ln x\,dx=x(\ln x-1)+C_{0))](https://wikimedia.org/api/rest_v1/media/math/render/svg/45ced9abfbe033de1dab09c1dfa704755885c317)
generalizes to
![{\displaystyle \int \dotsi \int \ln x\,dx\dotsm dx={\frac {x^{n)){n!))\left(\ln \,x-\sum _{k=1}^{n}{\frac {1}{k))\right)+\sum _{k=0}^{n-1}C_{k}{\frac {x^{k)){k!))}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8c34d7df20d2d235e0165f209c08efc563371bb3)