integral of (x^3+5x^2-2)

Lösung

\int (x^{3} + 5 x^{2} - 2) d x

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

Schritte zur Lösung

\int x^{3} + 5 x^{2} - 2 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 5 x^{2} d x - \int 2 d x

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

\int 5 x^{2} d x = \frac{5 x ^{3}}{3}

\int 2 d x = 2 x

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

Füge eine Konstante zur Lösung hinzu

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

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