What is the integral of 2e^{3x}-2x^{-1}+ln(4) ?

The integral of 2e^{3x}-2x^{-1}+ln(4) is 2/3 e^{3x}-2ln|x|+2ln(2)x+C

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integral of 2e^{3x}-2x^{-1}+ln(4)

\int 2 e^{3 x} - 2 x^{- 1} + ln (4) d x

\frac{2}{3} e^{3 x} - 2 ln ∣ x ∣ + 2 ln (2) x + C

Solution steps

\int 2 e^{3 x} - 2 x^{- 1} + ln (4) 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^{3 x} d x - \int 2 x^{- 1} d x + \int ln (4) d x

\int 2 e^{3 x} d x = \frac{2}{3} e^{3 x}

\int 2 x^{- 1} d x = 2 ln ∣ x ∣

\int ln (4) d x = 2 ln (2) x

= \frac{2}{3} e^{3 x} - 2 ln ∣ x ∣ + 2 ln (2) x

Add a constant to the solution

= \frac{2}{3} e^{3 x} - 2 ln ∣ x ∣ + 2 ln (2) x + C

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What is the integral of 2e^{3x}-2x^{-1}+ln(4) ?
The integral of 2e^{3x}-2x^{-1}+ln(4) is 2/3 e^{3x}-2ln|x|+2ln(2)x+C