What is the integral of 4/x+e^{-2x} ?

The integral of 4/x+e^{-2x} is 4ln|x|-1/2 e^{-2x}+C

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integral of 4/x+e^{-2x}

\int \frac{4}{x} + e^{- 2 x} d x

4 ln ∣ x ∣ - \frac{1}{2} e^{- 2 x} + C

Solution steps

\int \frac{4}{x} + e^{- 2 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 \frac{4}{x} d x + \int e^{- 2 x} d x

\int \frac{4}{x} d x = 4 ln ∣ x ∣

\int e^{- 2 x} d x = - \frac{1}{2} e^{- 2 x}

= 4 ln ∣ x ∣ - \frac{1}{2} e^{- 2 x}

Add a constant to the solution

= 4 ln ∣ x ∣ - \frac{1}{2} e^{- 2 x} + C

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What is the integral of 4/x+e^{-2x} ?
The integral of 4/x+e^{-2x} is 4ln|x|-1/2 e^{-2x}+C