integral of (1-\sqrt[3]{x})/(x^2)

Lösung

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

- \frac{1}{x} + \frac{3}{2 x ^{\frac{2}{3}}} + C

Schritte zur Lösung

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

Multipliziere aus

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

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

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

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

= - \frac{1}{x} - (- \frac{3}{2 x ^{\frac{2}{3}}})

Vereinfache

= - \frac{1}{x} + \frac{3}{2 x ^{\frac{2}{3}}}

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{x} + \frac{3}{2 x ^{\frac{2}{3}}} + C

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