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Beliebt Rechnen >

integral of 2x^3(3x^4-5)

Lösung

\int 2 x^{3} (3 x^{4} - 5) d x

Lösung

2 (\frac{1}{4} x^{4} (3 x^{4} - 5) - \frac{3 x ^{8}}{8}) + C

Schritte zur Lösung

\int 2 x^{3} (3 x^{4} - 5) d x

Entferne die Konstante:

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

= 2 \cdot \int x^{3} (3 x^{4} - 5) d x

Wende die partielle Integration an

= 2 (\frac{1}{4} x^{4} (3 x^{4} - 5) - \int 3 x^{7} d x)

\int 3 x^{7} d x = \frac{3 x ^{8}}{8}

= 2 (\frac{1}{4} x^{4} (3 x^{4} - 5) - \frac{3 x ^{8}}{8})

Füge eine Konstante zur Lösung hinzu

= 2 (\frac{1}{4} x^{4} (3 x^{4} - 5) - \frac{3 x ^{8}}{8}) + C

Graph

Beliebte Beispiele

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