What is the integral of (xe^{-x}) ?

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

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integral of (xe^{-x})

\int (x 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 y} (x y (x - 2) (y + 3))

x \to 0 lim (x^{2} + sin^{2} (x))

\frac{\partial}{\partial y} (2 arctan (\frac{x}{y}))

f (x) = (4 x + 5)^{2}

\int cos^{5} (x) tan^{3} (x) d x

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