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

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

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integral of-2xe^{-x}

\int - 2 x 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

\int_{1}^{2} (y^{3} + \frac{1}{4 y ^{3}}) d y

\frac{d y}{d x} = 9 y e^{x + 4}

\frac{d}{d x} (e^{- x + 3})

\frac{d}{d x} (cos^{2} (x^{2} - 2))

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

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