What is the integral of 2e^{-x}+6/x+ln(2) ?

The integral of 2e^{-x}+6/x+ln(2) is -2e^{-x}+6ln|x|+ln(2)x+C

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integral of 2e^{-x}+6/x+ln(2)

\int 2 e^{- x} + \frac{6}{x} + ln (2) d x

- 2 e^{- x} + 6 ln ∣ x ∣ + ln (2) x + C

Solution steps

\int 2 e^{- x} + \frac{6}{x} + ln (2) 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 2 e^{- x} d x + \int \frac{6}{x} d x + \int ln (2) d x

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

\int \frac{6}{x} d x = 6 ln ∣ x ∣

\int ln (2) d x = ln (2) x

= - 2 e^{- x} + 6 ln ∣ x ∣ + ln (2) x

Add a constant to the solution

= - 2 e^{- x} + 6 ln ∣ x ∣ + ln (2) x + C

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What is the integral of 2e^{-x}+6/x+ln(2) ?
The integral of 2e^{-x}+6/x+ln(2) is -2e^{-x}+6ln|x|+ln(2)x+C