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}})

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

\frac{d}{d x} ((\frac{- 2 x - 1}{- 4 x + 2})^{5})

\int_{2}^{4} 2 x^{2} - 3 x + 1 d x

\frac{\partial}{\partial x} (cos (x ln (y)))

x \to + 0 + lim (\frac{36 - 4 x ^{2}}{x})

\int 2 x 2 x - 1 d x