What is the integral of (150+20x)e^{-0.05x} ?

The integral of (150+20x)e^{-0.05x} is -400e^{-0.05x}x-11000e^{-0.05x}+C

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integral of (150+20x)e^{-0.05x}

\int (150 + 20 x) e^{- 0.05 x} d x

- 400 e^{- 0.05 x} x - 11000 e^{- 0.05 x} + C

Solution steps

\int (150 + 20 x) e^{- 0.05 x} d x

Apply Integration By Parts

: - 20 e^{- 0.05 x} (150 + 20 x) - \int - 400 e^{- 0.05 x} d x

= - 20 e^{- 0.05 x} (150 + 20 x) - \int - 400 e^{- 0.05 x} d x

\int - 400 e^{- 0.05 x} d x = 8000 e^{- 0.05 x}

= - 20 e^{- 0.05 x} (150 + 20 x) - 8000 e^{- 0.05 x}

Simplify

- 20 e^{- 0.05 x} (150 + 20 x) - 8000 e^{- 0.05 x} : - 400 e^{- 0.05 x} x - 11000 e^{- 0.05 x}

= - 400 e^{- 0.05 x} x - 11000 e^{- 0.05 x}

Add a constant to the solution

= - 400 e^{- 0.05 x} x - 11000 e^{- 0.05 x} + C

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What is the integral of (150+20x)e^{-0.05x} ?
The integral of (150+20x)e^{-0.05x} is -400e^{-0.05x}x-11000e^{-0.05x}+C