What is the integral of 100e^{-0.2x}-(50)/x ?

The integral of 100e^{-0.2x}-(50)/x is -500e^{-0.2x}-50ln|x|+C

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integral of 100e^{-0.2x}-(50)/x

\int 100 e^{- 0.2 x} - \frac{50}{x} d x

- 500 e^{- 0.2 x} - 50 ln ∣ x ∣ + C

Solution steps

\int 100 e^{- 0.2 x} - \frac{50}{x} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 100 e^{- 0.2 x} d x - \int \frac{50}{x} d x

\int 100 e^{- 0.2 x} d x = - 500 e^{- 0.2 x}

\int \frac{50}{x} d x = 50 ln ∣ x ∣

= - 500 e^{- 0.2 x} - 50 ln ∣ x ∣

Add a constant to the solution

= - 500 e^{- 0.2 x} - 50 ln ∣ x ∣ + C

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What is the integral of 100e^{-0.2x}-(50)/x ?
The integral of 100e^{-0.2x}-(50)/x is -500e^{-0.2x}-50ln|x|+C