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

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

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integral of xe^{-x/2}

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

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

Solution steps

\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

\int \frac{10}{1 + 4 x ^{2}} d x

\int \frac{x ^{2} + 6}{x ^{3} + x} d x

\frac{d}{d x} (\frac{5}{( 2 x - 3 ) ^{4}})

(0, 5), (10, 0)

\frac{\partial}{\partial x} (e^{5 x yz - 3})

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