What is the integral of y/(ln(y)) ?

The integral of y/(ln(y)) is \Ei(2ln(y))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of y/(ln(y))

\int \frac{y}{ln ( y )} d y

Ei (2 ln (y)) + C

Solution steps

\int \frac{y}{ln ( y )} d y

Apply u-substitution

= \int \frac{e ^{2 u}}{u} d u

Apply u-substitution

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

Use the nonelementary integral:

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

= Ei (v)

Substitute back

= Ei (2 ln (y))

Add a constant to the solution

= Ei (2 ln (y)) + C