What is the integral of 2x*e^{-x} ?

The integral of 2x*e^{-x} is 2(-e^{-x}x-e^{-x})+C

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integral of 2x*e^{-x}

\int 2 x \cdot e^{- x} d x

2 (- e^{- x} x - e^{- x}) + C

Solution steps

\int 2 x e^{- x} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int x e^{- x} d x

Apply Integration By Parts

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

= 2 (- e^{- x} x - \int - e^{- x} d x)

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

= 2 (- e^{- x} x - e^{- x})

Add a constant to the solution

= 2 (- e^{- x} x - e^{- x}) + C

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What is the integral of 2x*e^{-x} ?
The integral of 2x*e^{-x} is 2(-e^{-x}x-e^{-x})+C