What is the integral of [ 2/x+3e^x] ?

The integral of [ 2/x+3e^x] is 2ln|x|+3e^x+C

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integral of [ 2/x+3e^x]

\int [\frac{2}{x} + 3 e^{x}] d x

2 ln ∣ x ∣ + 3 e^{x} + C

Solution steps

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

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

= 2 ln ∣ x ∣ + 3 e^{x}

Add a constant to the solution

= 2 ln ∣ x ∣ + 3 e^{x} + C

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What is the integral of [ 2/x+3e^x] ?
The integral of [ 2/x+3e^x] is 2ln|x|+3e^x+C