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Beliebt Rechnen >

integral of x(\sqrt[3]{x}+\sqrt[4]{x})

Lösung

\int x (3 x + 4 x) d x

Lösung

\frac{3}{7} x^{\frac{7}{3}} + \frac{4}{9} x^{\frac{9}{4}} + C

Schritte zur Lösung

\int x (3 x + 4 x) d x

Multipliziere aus

x (3 x + 4 x) : x^{\frac{4}{3}} + x^{\frac{5}{4}}

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

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

\int x^{\frac{5}{4}} d x = \frac{4}{9} x^{\frac{9}{4}}

= \frac{3}{7} x^{\frac{7}{3}} + \frac{4}{9} x^{\frac{9}{4}}

Füge eine Konstante zur Lösung hinzu

= \frac{3}{7} x^{\frac{7}{3}} + \frac{4}{9} x^{\frac{9}{4}} + C

Graph

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