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Beliebt Rechnen >

integral of (u^{3/2}-3u+14)

Lösung

\int (u^{\frac{3}{2}} - 3 u + 14) d u

Lösung

\frac{2}{5} u^{\frac{5}{2}} - \frac{3 u ^{2}}{2} + 14 u + C

Schritte zur Lösung

\int u^{\frac{3}{2}} - 3 u + 14 d u

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int u^{\frac{3}{2}} d u - \int 3 u d u + \int 14 d u

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

\int 3 u d u = \frac{3 u ^{2}}{2}

\int 14 d u = 14 u

= \frac{2}{5} u^{\frac{5}{2}} - \frac{3 u ^{2}}{2} + 14 u

Füge eine Konstante zur Lösung hinzu

= \frac{2}{5} u^{\frac{5}{2}} - \frac{3 u ^{2}}{2} + 14 u + C

Graph

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