integral of (x-1)(x-4)

Lösung

\int (x - 1) (x - 4) d x

\frac{x ^{3}}{3} - \frac{5 x ^{2}}{2} + 4 x + C

Schritte zur Lösung

\int (x - 1) (x - 4) d x

Multipliziere aus

(x - 1) (x - 4) : x^{2} - 5 x + 4

= \int x^{2} - 5 x + 4 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 5 x d x + \int 4 d x

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

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

\int 4 d x = 4 x

= \frac{x ^{3}}{3} - \frac{5 x ^{2}}{2} + 4 x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{3}}{3} - \frac{5 x ^{2}}{2} + 4 x + C

\int \frac{22}{x 1 + 2 x} d x

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\frac{d}{d x} (x + \frac{4}{x + 3})

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