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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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{d y}{d x} = \frac{( y - 2 )}{( y - 1 )}

\frac{d}{d x} (\frac{4}{sec ( x )})

\int_{- 1}^{5} (1 + 4 x) d x

y^{^{''}} - 4 y^{^{'}} + 9 y = x e^{x}

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

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