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

Simplify

= \int e^{- \frac{x}{2}} x 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 8 e^{x} 9 + e^{x} d x

f (x) = \frac{x ^{7}}{7} - \frac{7}{x ^{7}}, at x = - 1

4

\frac{d}{d x} (x sin (x) - cos (x))

\int 8 x^{3} \cdot (2 x^{4} + 4)^{4} d x

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