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Beliebt Rechnen >

integral of 7\sqrt[4]{58-7x}-14

Lösung

\int 7 4 58 - 7 x - 14 d x

Lösung

- \frac{4}{5} (58 - 7 x)^{\frac{5}{4}} + 2 (58 - 7 x) + C

Schritte zur Lösung

\int 7 4 58 - 7 x - 14 d x

Wende U-Substitution an

= \int - 4 u + 2 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 4 u d u + \int 2 d u

\int 4 u d u = \frac{4}{5} u^{\frac{5}{4}}

\int 2 d u = 2 u

= - \frac{4}{5} u^{\frac{5}{4}} + 2 u

Setze in

u = 58 - 7 x

ein

= - \frac{4}{5} (58 - 7 x)^{\frac{5}{4}} + 2 (58 - 7 x)

Füge eine Konstante zur Lösung hinzu

= - \frac{4}{5} (58 - 7 x)^{\frac{5}{4}} + 2 (58 - 7 x) + C

Graph

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