What is the integral of (e^{1/y})/y ?

The integral of (e^{1/y})/y is -\Ei(1/y)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (e^{1/y})/y

integral

\frac{e ^{\frac{1}{y}}}{y}

- Ei (\frac{1}{y}) + C

Solution steps

\int \frac{e ^{\frac{1}{y}}}{y} d y

Apply u-substitution

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \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 = \frac{1}{y}

= - Ei (\frac{1}{y})

Add a constant to the solution

= - Ei (\frac{1}{y}) + C

What is the integral of (e^{1/y})/y ?
The integral of (e^{1/y})/y is -\Ei(1/y)+C