integral of (x+3)(3x-4)

Lösung

\int (x + 3) (3 x - 4) d x

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

Schritte zur Lösung

\int (x + 3) (3 x - 4) d x

Wende die partielle Integration an

= (3 x - 4) (\frac{x ^{2}}{2} + 3 x) - \int 3 (\frac{x ^{2}}{2} + 3 x) d x

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

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

Füge eine Konstante zur Lösung hinzu

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

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