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

Lösung

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

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

Schritte zur Lösung

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

Wende die Summenregel an:

\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})

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

= \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}})

t an g e n t x - x^{3}

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

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