What is the integral of-ye^{-y} ?

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

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integral of-ye^{-y}

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

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

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \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})

Simplify

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

Add a constant to the solution

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

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x \to + 2 lim (\frac{2 - x}{x ^{2} - 4})

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