integral of (x^2+x+5)

Lösung

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

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

Schritte zur Lösung

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

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

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

\int 5 d x = 5 x

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

Füge eine Konstante zur Lösung hinzu

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

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