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

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

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

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

- \frac{2}{x} + \frac{x ^{2}}{2} + C

Solution steps

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

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

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

= - \frac{2}{x} + \frac{x ^{2}}{2}

Add a constant to the solution

= - \frac{2}{x} + \frac{x ^{2}}{2} + C

\int x^{\frac{1}{4}} + 1 d x

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

\int x^{2} - 2 x - 1 d x

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

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

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