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

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

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

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

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

Solution steps

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

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

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

= \frac{x ^{2}}{2} - 2 ln ∣ x ∣ - e^{4 x}

Add a constant to the solution

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

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