What is the integral of x^{-1}e^x ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of x^{-1}e^x

integral

x^{- 1} e^{x}

Ei (x) + C

Solution steps

\int x^{- 1} e^{x} d x

Simplify

x^{- 1} e^{x} : \frac{e ^{x}}{x}

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

Use the nonelementary integral:

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

= Ei (x)

Add a constant to the solution

= Ei (x) + C

in t e g r a l (2 + x^{2})^{\frac{1}{2}}

in t e g r a l \frac{- 2}{z ^{3}}

in t e g r a l \frac{e ^{- 2} r}{a}

in t e g r a l 1 - x

in t e g r a l lo g_{10} (1 + x^{2})