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Beliebt Rechnen >

integral of (3x^5-x^3+6)

Lösung

\int (3 x^{5} - x^{3} + 6) d x

Lösung

\frac{x ^{6}}{2} - \frac{x ^{4}}{4} + 6 x + C

Schritte zur Lösung

\int 3 x^{5} - x^{3} + 6 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 3 x^{5} d x - \int x^{3} d x + \int 6 d x

\int 3 x^{5} d x = \frac{x ^{6}}{2}

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

\int 6 d x = 6 x

= \frac{x ^{6}}{2} - \frac{x ^{4}}{4} + 6 x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{6}}{2} - \frac{x ^{4}}{4} + 6 x + C

Graph

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