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

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

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integral of (2/x-4e^x)

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

2 ln ∣ x ∣ - 4 e^{x} + C

Solution steps

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

\int 4 e^{x} d x = 4 e^{x}

= 2 ln ∣ x ∣ - 4 e^{x}

Add a constant to the solution

= 2 ln ∣ x ∣ - 4 e^{x} + C

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