Primitives de fonctions logarithmes

$\int \frac{1}{\ln x}\,dx=\ln|\ln x|+\sum_{n=1}^{+\infty} \frac{(\ln x)^n}{nn!}+C$

$\int \frac{1}{x\ln x}\,dx=\ln|\ln x|+C$

$\int \frac{(\ln x)^n}{x}\,dx=\frac{1}{n+1}(\ln x)^{n+1}+C$ (n ∈ ℤ\{-1})

$\int x^m (\ln x)^n\,dx=\frac{x^{m+1}(\ln x)^n}{m+1}-\frac{n}{m+1}\int x^m(\ln x)^{n-1}\,dx$ (m, n ∈ ℤ\{-1})

On suppose a≠0.

$\int e^{ax}\ln x\,dx=\frac{1}{a}e^{ax}\ln |x|-\frac{1}{a}\int\frac{e^{ax}}{x}\,dx$

$\int \frac{x^m}{\ln\,x}\,dx=\ln|\ln\,x|+\sum_{n=1}^{+\infty}\frac{(m+1)^{n}(\ln\,x)^n}{n.n!}+C$(m ∈ ℤ)