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Beliebt Rechnen >

integral of (5x^2+7)/(x^{4/3)}

Lösung

\int \frac{5 x ^{2} + 7}{x ^{\frac{4}{3}}} d x

Lösung

3 x^{\frac{5}{3}} - \frac{21}{x ^{\frac{1}{3}}} + C

Schritte zur Lösung

\int \frac{5 x ^{2} + 7}{x ^{\frac{4}{3}}} d x

Multipliziere aus

\frac{5 x ^{2} + 7}{x ^{\frac{4}{3}}} : 5 x^{\frac{2}{3}} + \frac{7}{x ^{\frac{4}{3}}}

= \int 5 x^{\frac{2}{3}} + \frac{7}{x ^{\frac{4}{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 5 x^{\frac{2}{3}} d x + \int \frac{7}{x ^{\frac{4}{3}}} d x

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

\int \frac{7}{x ^{\frac{4}{3}}} d x = - \frac{21}{x ^{\frac{1}{3}}}

= 3 x^{\frac{5}{3}} - \frac{21}{x ^{\frac{1}{3}}}

Füge eine Konstante zur Lösung hinzu

= 3 x^{\frac{5}{3}} - \frac{21}{x ^{\frac{1}{3}}} + C

Graph

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