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Beliebt Rechnen >

integral of 3(x^5-x^3+1)

Lösung

\int 3 (x^{5} - x^{3} + 1) d x

Lösung

3 (\frac{x ^{6}}{6} - \frac{x ^{4}}{4} + x) + C

Schritte zur Lösung

\int 3 (x^{5} - x^{3} + 1) d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int x^{5} - x^{3} + 1 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

= 3 (\int x^{5} d x - \int x^{3} d x + \int 1 d x)

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

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

\int 1 d x = x

= 3 (\frac{x ^{6}}{6} - \frac{x ^{4}}{4} + x)

Füge eine Konstante zur Lösung hinzu

= 3 (\frac{x ^{6}}{6} - \frac{x ^{4}}{4} + x) + C

Graph

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