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

The integral of (x^4+2)/(x^2) is (x^3)/3-2/x+C

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

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

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

Solution steps

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

Expand

\frac{x ^{4} + 2}{x ^{2}} : x^{2} + \frac{2}{x ^{2}}

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

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

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

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

Add a constant to the solution

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

f (x) = x - 3, (7, 2)

\frac{d}{d x} (- \frac{6 x}{y})

\frac{9}{x}

x \to - 1 lim (\frac{1}{( x + 1 ) ^{2}})

\int x^{2} 1 0^{x^{3}} d x

What is the integral of (x^4+2)/(x^2) ?
The integral of (x^4+2)/(x^2) is (x^3)/3-2/x+C