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

= 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 cos ( x ) - 2 π}{x - 2 π}

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

(\frac{m ^{2} + 2}{2 m ^{3} + 4})^{^{'}}

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

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