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

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

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

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

3 ln ∣ x ∣ + 2 e^{x} + C

Solution steps

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

\int \frac{3}{x} d x = 3 ln ∣ x ∣

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

= 3 ln ∣ x ∣ + 2 e^{x}

Add a constant to the solution

= 3 ln ∣ x ∣ + 2 e^{x} + C

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