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

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

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

\int e^{- x} 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

= - 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

y = 3 x^{2} - 5 x, (2, 2)

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

\int (x + sin (y)) d x

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\int (\frac{x}{6})^{n} d x

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