What is the integral of (2e^x+3/x) ?

The integral of (2e^x+3/x) is 2e^x+3ln|x|+C

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integral of (2e^x+3/x)

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

2 e^{x} + 3 ln ∣ x ∣ + C

Solution steps

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

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

\int \frac{3}{x} d x = 3 ln ∣ x ∣

= 2 e^{x} + 3 ln ∣ x ∣

Add a constant to the solution

= 2 e^{x} + 3 ln ∣ x ∣ + C

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