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

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

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

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

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

Solution steps

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

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

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

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

Add a constant to the solution

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

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