What is the integral of e^{-x}*ln(x) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of e^{-x}*ln(x)

\int e^{- x} \cdot ln (x) d x

- e^{- x} ln (x) + Ei (- x) + C

Solution steps

\int e^{- x} ln (x) d x

Apply Integration By Parts

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

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

= - e^{- x} ln (x) - (- Ei (- x))

Simplify

= - e^{- x} ln (x) + Ei (- x)

Add a constant to the solution

= - e^{- x} ln (x) + Ei (- x) + C

What is the integral of e^{-x}*ln(x) ?
The integral of e^{-x}*ln(x) is -e^{-x}ln(x)+\Ei(-x)+C