What is the integral of 1/4 (e^x+2/x) ?

The integral of 1/4 (e^x+2/x) is 1/4 (e^x+2ln|x|)+C

integral of 1/4 (e^x+2/x)

\int \frac{1}{4} (e^{x} + \frac{2}{x}) d x

\frac{1}{4} (e^{x} + 2 ln ∣ x ∣) + C

Solution steps

\int \frac{1}{4} (e^{x} + \frac{2}{x}) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{4} \cdot \int e^{x} + \frac{2}{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

= \frac{1}{4} (\int e^{x} d x + \int \frac{2}{x} d x)

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

= \frac{1}{4} (e^{x} + 2 ln ∣ x ∣)

Add a constant to the solution

= \frac{1}{4} (e^{x} + 2 ln ∣ x ∣) + C

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What is the integral of 1/4 (e^x+2/x) ?
The integral of 1/4 (e^x+2/x) is 1/4 (e^x+2ln|x|)+C