What is the integral of xe^{-x/6} ?

The integral of xe^{-x/6} is -6e^{-x/6}x-36e^{-x/6}+C

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integral of xe^{-x/6}

\int x e^{- \frac{x}{6}} d x

- 6 e^{- \frac{x}{6}} x - 36 e^{- \frac{x}{6}} + C

Solution steps

\int x e^{- \frac{x}{6}} d x

Apply Integration By Parts

: - 6 e^{- \frac{x}{6}} x - \int - 6 e^{- \frac{x}{6}} d x

= - 6 e^{- \frac{x}{6}} x - \int - 6 e^{- \frac{x}{6}} d x

\int - 6 e^{- \frac{x}{6}} d x = 36 e^{- \frac{x}{6}}

= - 6 e^{- \frac{x}{6}} x - 36 e^{- \frac{x}{6}}

Add a constant to the solution

= - 6 e^{- \frac{x}{6}} x - 36 e^{- \frac{x}{6}} + C

\frac{d}{d x} ((2 x - 5)^{\frac{1}{2}})

\int y^{2} e^{- 2 y} d y

f (x) = x e^{\frac{1}{x}}

- cos (x), [0, π]

\frac{\partial}{\partial x} (2 y + x e^{y})

What is the integral of xe^{-x/6} ?
The integral of xe^{-x/6} is -6e^{-x/6}x-36e^{-x/6}+C