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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

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