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

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

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integral of xe^{-1/2 x}

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

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

Solution steps

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

Simplify

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

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

Add a constant to the solution

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

x \to 2 lim (1 0^{x^{2} - 4 x})

\int e x^{e + 1} d x

f (x) = 2 x 1 - x^{2}

f (x) = (8 x^{2} - 13 x) e^{x}

\int_{0}^{5} 25 + x^{2} d x

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