integral of (sqrt(x)-2x^2)/(x^3)

Lösung

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

- \frac{2}{3 x ^{\frac{3}{2}}} - 2 ln ∣ x ∣ + C

Schritte zur Lösung

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

Multipliziere aus

\frac{x - 2 x ^{2}}{x ^{3}} : \frac{1}{x ^{\frac{5}{2}}} - \frac{2}{x}

= \int \frac{1}{x ^{\frac{5}{2}}} - \frac{2}{x} 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 ^{\frac{5}{2}}} d x - \int \frac{2}{x} d x

\int \frac{1}{x ^{\frac{5}{2}}} d x = - \frac{2}{3 x ^{\frac{3}{2}}}

\int \frac{2}{x} d x = 2 ln ∣ x ∣

= - \frac{2}{3 x ^{\frac{3}{2}}} - 2 ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= - \frac{2}{3 x ^{\frac{3}{2}}} - 2 ln ∣ x ∣ + C

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