integral of (x+3)(x+7)

Lösung

\int (x + 3) (x + 7) d x

\frac{x ^{3}}{3} + 5 x^{2} + 21 x + C

Schritte zur Lösung

\int (x + 3) (x + 7) d x

Multipliziere aus

(x + 3) (x + 7) : x^{2} + 10 x + 21

= \int x^{2} + 10 x + 21 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 10 x d x + \int 21 d x

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

\int 10 x d x = 5 x^{2}

\int 21 d x = 21 x

= \frac{x ^{3}}{3} + 5 x^{2} + 21 x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{3}}{3} + 5 x^{2} + 21 x + C

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