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Beliebt Rechnen >

integral of 4x^3(x^4-8)

Lösung

\int 4 x^{3} (x^{4} - 8) d x

Lösung

4 (\frac{x ^{8}}{8} - 2 x^{4}) + C

Schritte zur Lösung

\int 4 x^{3} (x^{4} - 8) d x

Entferne die Konstante:

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

= 4 \cdot \int x^{3} (x^{4} - 8) d x

Multipliziere aus

x^{3} (x^{4} - 8) : x^{7} - 8 x^{3}

= 4 \cdot \int x^{7} - 8 x^{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

= 4 (\int x^{7} d x - \int 8 x^{3} d x)

\int x^{7} d x = \frac{x ^{8}}{8}

\int 8 x^{3} d x = 2 x^{4}

= 4 (\frac{x ^{8}}{8} - 2 x^{4})

Füge eine Konstante zur Lösung hinzu

= 4 (\frac{x ^{8}}{8} - 2 x^{4}) + C

Graph

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