What is the integral of 0.775e^{-0.05x}(20-x) ?

The integral of 0.775e^{-0.05x}(20-x) is 15.5e^{-0.05x}x+C

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integral of 0.775e^{-0.05x}(20-x)

\int 0.775 e^{- 0.05 x} (20 - x) d x

15.5 e^{- 0.05 x} x + C

Solution steps

\int 0.775 e^{- 0.05 x} (20 - x) d x

Take the constant out:

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

= 0.775 \cdot \int e^{- 0.05 x} (20 - x) d x

Apply Integration By Parts

: - 20 e^{- 0.05 x} (20 - x) - \int 20 e^{- 0.05 x} d x

= 0.775 (- 20 e^{- 0.05 x} (20 - x) - \int 20 e^{- 0.05 x} d x)

\int 20 e^{- 0.05 x} d x = - 400 e^{- 0.05 x}

= 0.775 (- 20 e^{- 0.05 x} (20 - x) - (- 400 e^{- 0.05 x}))

Simplify

0.775 (- 20 e^{- 0.05 x} (20 - x) - (- 400 e^{- 0.05 x})) : 15.5 e^{- 0.05 x} x

= 15.5 e^{- 0.05 x} x

Add a constant to the solution

= 15.5 e^{- 0.05 x} x + C

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What is the integral of 0.775e^{-0.05x}(20-x) ?
The integral of 0.775e^{-0.05x}(20-x) is 15.5e^{-0.05x}x+C