What is the integral of 20(35-x)e^{-x/(25)} ?

The integral of 20(35-x)e^{-x/(25)} is 20(25e^{-x/(25)}x-250e^{-x/(25)})+C

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integral of 20(35-x)e^{-x/(25)}

\int 20 (35 - x) e^{- \frac{x}{25}} d x

20 (25 e^{- \frac{x}{25}} x - 250 e^{- \frac{x}{25}}) + C

Solution steps

\int 20 (35 - x) e^{- \frac{x}{25}} d x

Take the constant out:

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

= 20 \cdot \int (35 - x) e^{- \frac{x}{25}} d x

Apply Integration By Parts

: - 25 e^{- \frac{x}{25}} (35 - x) - \int 25 e^{- \frac{x}{25}} d x

= 20 (- 25 e^{- \frac{x}{25}} (35 - x) - \int 25 e^{- \frac{x}{25}} d x)

\int 25 e^{- \frac{x}{25}} d x = - 625 e^{- \frac{x}{25}}

= 20 (- 25 e^{- \frac{x}{25}} (35 - x) - (- 625 e^{- \frac{x}{25}}))

Simplify

20 (- 25 e^{- \frac{x}{25}} (35 - x) - (- 625 e^{- \frac{x}{25}})) : 20 (25 e^{- \frac{x}{25}} x - 250 e^{- \frac{x}{25}})

= 20 (25 e^{- \frac{x}{25}} x - 250 e^{- \frac{x}{25}})

Add a constant to the solution

= 20 (25 e^{- \frac{x}{25}} x - 250 e^{- \frac{x}{25}}) + C

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What is the integral of 20(35-x)e^{-x/(25)} ?
The integral of 20(35-x)e^{-x/(25)} is 20(25e^{-x/(25)}x-250e^{-x/(25)})+C