What is the integral of (x^2)/2+1/(2x^2) ?

The integral of (x^2)/2+1/(2x^2) is (x^3)/6-1/(2x)+C

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integral of (x^2)/2+1/(2x^2)

\int \frac{x ^{2}}{2} + \frac{1}{2 x ^{2}} d x

\frac{x ^{3}}{6} - \frac{1}{2 x} + C

Solution steps

\int \frac{x ^{2}}{2} + \frac{1}{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{1}{2 x ^{2}} d x

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

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

= \frac{x ^{3}}{6} - \frac{1}{2 x}

Add a constant to the solution

= \frac{x ^{3}}{6} - \frac{1}{2 x} + C

What is the integral of (x^2)/2+1/(2x^2) ?
The integral of (x^2)/2+1/(2x^2) is (x^3)/6-1/(2x)+C