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Beliebt Rechnen >

integral of (6x+12)(x-3)

Lösung

\int (6 x + 12) (x - 3) d x

Lösung

2 x^{3} - 3 x^{2} - 36 x + C

Schritte zur Lösung

\int (6 x + 12) (x - 3) d x

Wende die partielle Integration an

= (6 x + 12) (\frac{x ^{2}}{2} - 3 x) - \int 6 (\frac{x ^{2}}{2} - 3 x) d x

\int 6 (\frac{x ^{2}}{2} - 3 x) d x = x^{3} - 9 x^{2}

= (6 x + 12) (\frac{x ^{2}}{2} - 3 x) - (x^{3} - 9 x^{2})

Vereinfache

(6 x + 12) (\frac{x ^{2}}{2} - 3 x) - (x^{3} - 9 x^{2}) : 2 x^{3} - 3 x^{2} - 36 x

= 2 x^{3} - 3 x^{2} - 36 x

Füge eine Konstante zur Lösung hinzu

= 2 x^{3} - 3 x^{2} - 36 x + C

Graph

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