What is the integral of y/(e^{-y)} ?

The integral of y/(e^{-y)} is e^yy-e^y+C

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integral of y/(e^{-y)}

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

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

Solution steps

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

Apply Integration By Parts

= 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

f (x) = \frac{x - x ^{2}}{x ^{3} + 2}

y^{^{''}} + 9 y = 4 cos (2 x)

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

y^{^{''}} - 4 y = 9 e^{t}, y (0) = 0, y^{^{'}} (0) = 0

x \to - 1 lim (5 - 2 x - x^{2})