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

The integral of ((x^2)/2-2/(x^2)) is (x^3)/6+2/x+C

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

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

\frac{x ^{3}}{6} + \frac{2}{x} + C

Solution steps

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

\int \frac{x ^{2}}{2} d x = \frac{x ^{3}}{6}

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

= \frac{x ^{3}}{6} - (- \frac{2}{x})

Simplify

= \frac{x ^{3}}{6} + \frac{2}{x}

Add a constant to the solution

= \frac{x ^{3}}{6} + \frac{2}{x} + C

\frac{\partial}{\partial x} (\frac{3 y}{x ^{2} + 2})

\frac{d}{d x} (\frac{3}{4} x^{\frac{4}{3}} - \frac{3}{8} x^{\frac{2}{3}})

x - x^{3}

\frac{d}{d x} (\frac{x}{( 1 + x )})

\int \frac{x ^{2} + 3 x + 2}{x ^{2} ( x + 3 )} d x

What is the integral of ((x^2)/2-2/(x^2)) ?
The integral of ((x^2)/2-2/(x^2)) is (x^3)/6+2/x+C