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

Lösung

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

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

Schritte zur Lösung

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

Multipliziere aus

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

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

\frac{d}{d x} (\frac{- 1 - x}{( x - 1 ) ^{3}})

\int \frac{( x ^{2} + x + 1 )}{x ^{2} + 1} d x

\frac{d}{d x} (ln (e^{4}))

\frac{d}{d x} (5 x^{3} - x^{- \frac{2}{5}})

x \to 0 lim (12 + x^{2} ln (x))