What is the integral of (3e^x+4/x) ?

The integral of (3e^x+4/x) is 3e^x+4ln|x|+C

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integral of (3e^x+4/x)

\int (3 e^{x} + \frac{4}{x}) d x

3 e^{x} + 4 ln ∣ x ∣ + C

Solution steps

\int 3 e^{x} + \frac{4}{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 3 e^{x} d x + \int \frac{4}{x} d x

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

\int \frac{4}{x} d x = 4 ln ∣ x ∣

= 3 e^{x} + 4 ln ∣ x ∣

Add a constant to the solution

= 3 e^{x} + 4 ln ∣ x ∣ + C

What is the integral of (3e^x+4/x) ?
The integral of (3e^x+4/x) is 3e^x+4ln|x|+C