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

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

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

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

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

Solution steps

\int ln (x) e^{- 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

\int \frac{4 x ^{2} + 3}{( x - 5 ) ^{2}} d x

\frac{d}{d x} (\frac{( x + 5 ) ( x ^{2} - 5 x + 25 )}{x ^{3}})

\int x^{2} x^{3} + 1 d x

\frac{d}{d x} (3 x^{2} - x)

f (x) = 2000 (x^{2} + 5)^{\frac{1}{3}}

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