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

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

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integral of 6xe^{-x/6}

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

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

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 6 \cdot \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 (- 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 (- 6 e^{- \frac{x}{6}} x - 36 e^{- \frac{x}{6}})

Add a constant to the solution

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

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