What is the integral of xe^{-x/(10)} ?

The integral of xe^{-x/(10)} is -10e^{-x/(10)}x-100e^{-x/(10)}+C

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integral of xe^{-x/(10)}

\int x e^{- \frac{x}{10}} d x

- 10 e^{- \frac{x}{10}} x - 100 e^{- \frac{x}{10}} + C

Solution steps

\int x e^{- \frac{x}{10}} d x

Apply Integration By Parts

: - 10 e^{- \frac{x}{10}} x - \int - 10 e^{- \frac{x}{10}} d x

= - 10 e^{- \frac{x}{10}} x - \int - 10 e^{- \frac{x}{10}} d x

\int - 10 e^{- \frac{x}{10}} d x = 100 e^{- \frac{x}{10}}

= - 10 e^{- \frac{x}{10}} x - 100 e^{- \frac{x}{10}}

Add a constant to the solution

= - 10 e^{- \frac{x}{10}} x - 100 e^{- \frac{x}{10}} + C

\int_{0}^{2} 2 e^{x} d x

(3 t - 1) (2 t - 2)^{- 1}

x \to 2 lim (3 x^{2} - 4 x + 5)

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

\int \frac{30 x ^{5}}{2 + 5 x ^{6}} d x

What is the integral of xe^{-x/(10)} ?
The integral of xe^{-x/(10)} is -10e^{-x/(10)}x-100e^{-x/(10)}+C