What is the integral of (-xe^{-x})/(-4) ?

The integral of (-xe^{-x})/(-4) is 1/4 (-e^{-x}x-e^{-x})+C

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integral of (-xe^{-x})/(-4)

\int \frac{- x e ^{- x}}{- 4} d x

\frac{1}{4} (- e^{- x} x - e^{- x}) + C

Solution steps

\int \frac{- x e ^{- x}}{- 4} d x

Take the constant out:

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

= \frac{- 1}{- 4} \cdot \int x e^{- x} d x

Simplify

= \frac{1}{4} \cdot \int x e^{- x} d x

Apply Integration By Parts

= \frac{1}{4} (- e^{- x} x - \int - e^{- x} d x)

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

= \frac{1}{4} (- e^{- x} x - e^{- x})

Add a constant to the solution

= \frac{1}{4} (- e^{- x} x - e^{- x}) + C

What is the integral of (-xe^{-x})/(-4) ?
The integral of (-xe^{-x})/(-4) is 1/4 (-e^{-x}x-e^{-x})+C