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

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

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integral of (4/x+e^{2x})

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

4 ln ∣ x ∣ + \frac{1}{2} e^{2 x} + C

Solution steps

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

\int \frac{4}{x} d x = 4 ln ∣ x ∣

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

= 4 ln ∣ x ∣ + \frac{1}{2} e^{2 x}

Add a constant to the solution

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

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