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Beliebt Rechnen >

integral of 4x^3-\sqrt[3]{x}+x^e

Lösung

\int 4 x^{3} - 3 x + x^{e} d x

Lösung

x^{4} - \frac{3}{4} x^{\frac{4}{3}} + \frac{x ^{e + 1}}{e + 1} + C

Schritte zur Lösung

\int 4 x^{3} - 3 x + x^{e} 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 4 x^{3} d x - \int 3 x d x + \int x^{e} d x

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

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

\int x^{e} d x = \frac{x ^{e + 1}}{e + 1}

= x^{4} - \frac{3}{4} x^{\frac{4}{3}} + \frac{x ^{e + 1}}{e + 1}

Füge eine Konstante zur Lösung hinzu

= x^{4} - \frac{3}{4} x^{\frac{4}{3}} + \frac{x ^{e + 1}}{e + 1} + C

Graph

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