integral of (x+2)/(x^3)

Lösung

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

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

Schritte zur Lösung

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

Multipliziere aus

\frac{x + 2}{x ^{3}} : \frac{1}{x ^{2}} + \frac{2}{x ^{3}}

= \int \frac{1}{x ^{2}} + \frac{2}{x ^{3}} 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{1}{x ^{2}} d x + \int \frac{2}{x ^{3}} d x

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

\int \frac{2}{x ^{3}} d x = - \frac{1}{x ^{2}}

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

Füge eine Konstante zur Lösung hinzu

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

\frac{\partial}{\partial x} (2 x e^{x^{2}})

\int (sec^{2} (π x) - x) d x

\frac{\partial}{\partial x} ((\frac{y x}{z w})^{\frac{1}{2}})

\frac{d}{d x} (\frac{4 - x e ^{x}}{x + e ^{x}})

n = 1 \sum \infty \frac{cos ( nπ )}{n ^{2}}