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

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

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integral of ye^{y-x}

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

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