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} \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

= - 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

\frac{\partial}{\partial x} (x^{2} y - y^{2})

\int \frac{sec ( x )}{sec ( x ) + tan ( x )} d x

x \to 2 + lim (\frac{3}{x - 2})

\frac{\partial}{\partial z} (3 z e^{x yz})

\frac{d ^{3}}{d x ^{3}} (sin (3 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