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Beliebt Rechnen >

integral of (p^2-9p)/(\sqrt[5]{p)}

Lösung

\int \frac{p ^{2} - 9 p}{5 p} d p

Lösung

\frac{5}{14} p^{\frac{14}{5}} - 5 p^{\frac{9}{5}} + C

Schritte zur Lösung

\int \frac{p ^{2} - 9 p}{5 p} d p

Multipliziere aus

\frac{p ^{2} - 9 p}{5 p} : \frac{p ^{2}}{5 p} - \frac{9 p}{5 p}

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{p ^{2}}{5 p} d p - \int \frac{9 p}{5 p} d p

\int \frac{p ^{2}}{5 p} d p = \frac{5}{14} p^{\frac{14}{5}}

\int \frac{9 p}{5 p} d p = 5 p^{\frac{9}{5}}

= \frac{5}{14} p^{\frac{14}{5}} - 5 p^{\frac{9}{5}}

Füge eine Konstante zur Lösung hinzu

= \frac{5}{14} p^{\frac{14}{5}} - 5 p^{\frac{9}{5}} + C

Graph

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