What is the integral of 30(10-x)e^{-x/(30)} ?

The integral of 30(10-x)e^{-x/(30)} is 30(30e^{-x/(30)}x+600e^{-x/(30)})+C

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integral of 30(10-x)e^{-x/(30)}

\int 30 (10 - x) e^{- \frac{x}{30}} d x

30 (30 e^{- \frac{x}{30}} x + 600 e^{- \frac{x}{30}}) + C

Solution steps

\int 30 (10 - x) e^{- \frac{x}{30}} d x

Take the constant out:

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

= 30 \cdot \int (10 - x) e^{- \frac{x}{30}} d x

Apply Integration By Parts

= 30 (- 30 e^{- \frac{x}{30}} (10 - x) - \int 30 e^{- \frac{x}{30}} d x)

\int 30 e^{- \frac{x}{30}} d x = - 900 e^{- \frac{x}{30}}

= 30 (- 30 e^{- \frac{x}{30}} (10 - x) - (- 900 e^{- \frac{x}{30}}))

Simplify

30 (- 30 e^{- \frac{x}{30}} (10 - x) - (- 900 e^{- \frac{x}{30}})) : 30 (30 e^{- \frac{x}{30}} x + 600 e^{- \frac{x}{30}})

= 30 (30 e^{- \frac{x}{30}} x + 600 e^{- \frac{x}{30}})

Add a constant to the solution

= 30 (30 e^{- \frac{x}{30}} x + 600 e^{- \frac{x}{30}}) + C

What is the integral of 30(10-x)e^{-x/(30)} ?
The integral of 30(10-x)e^{-x/(30)} is 30(30e^{-x/(30)}x+600e^{-x/(30)})+C