What is the integral of y*e^{-y} ?

The integral of y*e^{-y} is -e^{-y}y-e^{-y}+C

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integral of y*e^{-y}

\int y \cdot e^{- y} d y

- e^{- y} y - e^{- y} + C

Solution steps

\int y e^{- y} d y

Apply Integration By Parts

: - e^{- y} y - \int - e^{- y} d y

= - e^{- y} y - \int - e^{- y} d y

\int - e^{- y} d y = e^{- y}

= - e^{- y} y - e^{- y}

Add a constant to the solution

= - e^{- y} y - e^{- y} + C

(2 y + 2 t - 9) d t + (8 y + 2 t - 1) d y = 0

\frac{d}{d x} (\frac{7 x}{x - 1})

x \to 0 lim (x^{x})

\int sec^{2} (\frac{x}{3}) d x

\frac{\partial}{\partial x} (ln (4 x))

What is the integral of y*e^{-y} ?
The integral of y*e^{-y} is -e^{-y}y-e^{-y}+C