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Beliebt Rechnen >

integral of (x^5-3x^4+6x^3+3)

Lösung

\int (x^{5} - 3 x^{4} + 6 x^{3} + 3) d x

Lösung

\frac{x ^{6}}{6} - \frac{3 x ^{5}}{5} + \frac{3 x ^{4}}{2} + 3 x + C

Schritte zur Lösung

\int x^{5} - 3 x^{4} + 6 x^{3} + 3 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^{5} d x - \int 3 x^{4} d x + \int 6 x^{3} d x + \int 3 d x

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

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

\int 6 x^{3} d x = \frac{3 x ^{4}}{2}

\int 3 d x = 3 x

= \frac{x ^{6}}{6} - \frac{3 x ^{5}}{5} + \frac{3 x ^{4}}{2} + 3 x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{6}}{6} - \frac{3 x ^{5}}{5} + \frac{3 x ^{4}}{2} + 3 x + C

Graph

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