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Beliebt Rechnen >

integral of 12x^2(4x^3-3)

Lösung

\int 12 x^{2} (4 x^{3} - 3) d x

Lösung

12 (\frac{4}{3} x^{6} - x^{3} - \frac{2 x ^{6}}{3}) + C

Schritte zur Lösung

\int 12 x^{2} (4 x^{3} - 3) d x

Entferne die Konstante:

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

= 12 \cdot \int x^{2} (4 x^{3} - 3) d x

Wende die partielle Integration an

= 12 (\frac{1}{3} x^{3} (4 x^{3} - 3) - \int 4 x^{5} d x)

\int 4 x^{5} d x = \frac{2 x ^{6}}{3}

= 12 (\frac{1}{3} x^{3} (4 x^{3} - 3) - \frac{2 x ^{6}}{3})

Multipliziere aus

\frac{1}{3} x^{3} (4 x^{3} - 3) : \frac{4}{3} x^{6} - x^{3}

= 12 (\frac{4}{3} x^{6} - x^{3} - \frac{2 x ^{6}}{3})

Füge eine Konstante zur Lösung hinzu

= 12 (\frac{4}{3} x^{6} - x^{3} - \frac{2 x ^{6}}{3}) + C

Graph

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