What is the integral of-2xe^{-1/2 x} ?

The integral of-2xe^{-1/2 x} is -2(-2e^{-x/2}x-4e^{-x/2})+C

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integral of-2xe^{-1/2 x}

\int - 2 x e^{- \frac{1}{2} x} d x

- 2 (- 2 e^{- \frac{x}{2}} x - 4 e^{- \frac{x}{2}}) + C

Solution steps

\int - 2 x e^{- \frac{1}{2} 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^{- \frac{1}{2} x} d x

Simplify

- \frac{1}{2} x : - \frac{x}{2}

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

Apply Integration By Parts

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

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

\int - 2 e^{- \frac{x}{2}} d x = 4 e^{- \frac{x}{2}}

= - 2 (- 2 e^{- \frac{x}{2}} x - 4 e^{- \frac{x}{2}})

Add a constant to the solution

= - 2 (- 2 e^{- \frac{x}{2}} x - 4 e^{- \frac{x}{2}}) + C

\frac{\partial}{\partial x} (cos (x^{2}))

\int \frac{x ^{2} + 3 x - 2}{x} d x

\int \frac{2 x}{x ^{4} + 1} d x

\int 5 x^{2} a^{2} - x^{2} d x

x \to \frac{π}{6} lim (cot (2 x))

What is the integral of-2xe^{-1/2 x} ?
The integral of-2xe^{-1/2 x} is -2(-2e^{-x/2}x-4e^{-x/2})+C