integral of (x+2)^2(x-3)^3

Lösung

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

\frac{x ^{6}}{6} - x^{5} - \frac{5 x ^{4}}{4} + 15 x^{3} - 108 x + C

Schritte zur Lösung

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

Multipliziere aus

(x + 2)^{2} (x - 3)^{3} : x^{5} - 5 x^{4} - 5 x^{3} + 45 x^{2} - 108

= \int x^{5} - 5 x^{4} - 5 x^{3} + 45 x^{2} - 108 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^{5} d x - \int 5 x^{4} d x - \int 5 x^{3} d x + \int 45 x^{2} d x - \int 108 d x

\int x^{5} d x = \frac{x ^{6}}{6}

\int 5 x^{4} d x = x^{5}

\int 5 x^{3} d x = \frac{5 x ^{4}}{4}

\int 45 x^{2} d x = 15 x^{3}

\int 108 d x = 108 x

= \frac{x ^{6}}{6} - x^{5} - \frac{5 x ^{4}}{4} + 15 x^{3} - 108 x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{6}}{6} - x^{5} - \frac{5 x ^{4}}{4} + 15 x^{3} - 108 x + C

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