What is the integral of e^{-3x}+ln(3)-1/x ?

The integral of e^{-3x}+ln(3)-1/x is -1/3 e^{-3x}+ln(3)x-ln|x|+C

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integral of e^{-3x}+ln(3)-1/x

\int e^{- 3 x} + ln (3) - \frac{1}{x} d x

- \frac{1}{3} e^{- 3 x} + ln (3) x - ln ∣ x ∣ + C

Solution steps

\int e^{- 3 x} + ln (3) - \frac{1}{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 e^{- 3 x} d x + \int ln (3) d x - \int \frac{1}{x} d x

\int e^{- 3 x} d x = - \frac{1}{3} e^{- 3 x}

\int ln (3) d x = ln (3) x

\int \frac{1}{x} d x = ln ∣ x ∣

= - \frac{1}{3} e^{- 3 x} + ln (3) x - ln ∣ x ∣

Add a constant to the solution

= - \frac{1}{3} e^{- 3 x} + ln (3) x - ln ∣ x ∣ + C

What is the integral of e^{-3x}+ln(3)-1/x ?
The integral of e^{-3x}+ln(3)-1/x is -1/3 e^{-3x}+ln(3)x-ln|x|+C