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

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

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integral of x*e^{-x}

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

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

Solution steps

\int x e^{- x} d x

Apply Integration By Parts

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

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

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

= - e^{- x} x - e^{- x}

Add a constant to the solution

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

\frac{\partial}{\partial x} (x^{0.5} \cdot y)

x \to 0 lim (csc (x))

\int x^{2} 4 x + 4 d x

cos (3 t) sin (2 t)

x^{2} - y^{2} = 16, (5, 3)

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