integral of (x-1)(x+3)

Lösung

\int (x - 1) (x + 3) d x

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

Schritte zur Lösung

\int (x - 1) (x + 3) d x

Multipliziere aus

(x - 1) (x + 3) : x^{2} + 2 x - 3

= \int x^{2} + 2 x - 3 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 2 x d x - \int 3 d x

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

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

\int 3 d x = 3 x

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

Füge eine Konstante zur Lösung hinzu

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

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