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

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

\frac{d}{d x} (cos^{2} (sin (4 x)))

y^{^{''}} + 5 y^{^{'}} + 6 y = 2 e^{x}, y (0) = 1, y^{^{'}} (0) = - 1

\int 4 sin (5 x) + 5 cos (3 x) d x

\frac{d y}{d t} = 2 y - t

\frac{d}{d x} ((1 + x^{2})^{5})