What is the integral from 0 to 2x of ye^{y-x} ?

The integral from 0 to 2x of ye^{y-x} is 2xe^x-e^x+e^{-x}

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integral from 0 to 2x of ye^{y-x}

\int_{0}^{2 x} y e^{y - x} d y

2 x e^{x} - e^{x} + e^{- x}

Solution steps

\int_{0}^{2 x} y e^{y - x} d y

Apply Integration By Parts

: [e^{- x + y} y - \int e^{- x + y} d y]_{0}^{2 x}

= [e^{- x + y} y - \int e^{- x + y} d y]_{0}^{2 x}

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

= [e^{- x + y} y - e^{- x + y}]_{0}^{2 x}

Compute the boundaries:

2 x e^{x} - e^{x} + e^{- x}

= 2 x e^{x} - e^{x} + e^{- x}

\int_{1}^{6} x^{2} - 4 x - 12 d x

\int_{- 1}^{2} \frac{1}{x ^{2} - 9} d x

\int_{0}^{1} x + x^{2} d x

\int_{0}^{3} t 1 + 4 t^{2} d t

\int_{0}^{0.5} \frac{1}{x ln ^{2} ∣ x ∣} d x

What is the integral from 0 to 2x of ye^{y-x} ?
The integral from 0 to 2x of ye^{y-x} is 2xe^x-e^x+e^{-x}