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

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

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integral of (1/x+2e^{2x})

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

ln ∣ x ∣ + e^{2 x} + C

Solution steps

\int \frac{1}{x} + 2 e^{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

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

\int \frac{1}{x} d x = ln ∣ x ∣

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

= ln ∣ x ∣ + e^{2 x}

Add a constant to the solution

= ln ∣ x ∣ + e^{2 x} + C

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