What is the integral of 1/(ln(x)) ?

The integral of 1/(ln(x)) is \Ei(ln(x))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 1/(ln(x))

integral

\frac{1}{ln ( x )}

Ei (ln (x)) + C

Solution steps

\int \frac{1}{ln ( x )} d x

Apply u-substitution

= \int \frac{e ^{u}}{u} d u

Use the nonelementary integral:

\int \frac{e ^{x}}{x} d x = Ei (x)

= Ei (u)

Substitute back

u = ln (x)

= Ei (ln (x))

Add a constant to the solution

= Ei (ln (x)) + C