What is the integral of (e^x+1/(3x)) ?

The integral of (e^x+1/(3x)) is e^x+1/3 ln|x|+C

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integral of (e^x+1/(3x))

\int (e^{x} + \frac{1}{3 x}) d x

e^{x} + \frac{1}{3} ln ∣ x ∣ + C

Solution steps

\int e^{x} + \frac{1}{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 e^{x} d x + \int \frac{1}{3 x} d x

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

\int \frac{1}{3 x} d x = \frac{1}{3} ln ∣ x ∣

= e^{x} + \frac{1}{3} ln ∣ x ∣

Add a constant to the solution

= e^{x} + \frac{1}{3} ln ∣ x ∣ + C

What is the integral of (e^x+1/(3x)) ?
The integral of (e^x+1/(3x)) is e^x+1/3 ln|x|+C