integral of (x+7)(x-6)

Lösung

\int (x + 7) (x - 6) d x

\frac{x ^{3}}{3} + \frac{x ^{2}}{2} - 42 x + C

Schritte zur Lösung

\int (x + 7) (x - 6) d x

Multipliziere aus

(x + 7) (x - 6) : x^{2} + x - 42

= \int x^{2} + x - 42 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

= \int x^{2} d x + \int x d x - \int 42 d x

\int x^{2} d x = \frac{x ^{3}}{3}

\int x d x = \frac{x ^{2}}{2}

\int 42 d x = 42 x

= \frac{x ^{3}}{3} + \frac{x ^{2}}{2} - 42 x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{3}}{3} + \frac{x ^{2}}{2} - 42 x + C

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