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Beliebt Rechnen >

integral of (x^3+8)/(x+2)

Lösung

\int \frac{x ^{3} + 8}{x + 2} d x

Lösung

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

Schritte zur Lösung

\int \frac{x ^{3} + 8}{x + 2} d x

Vereinfache

\frac{x ^{3} + 8}{x + 2} : x^{2} - 2 x + 4

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

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

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

\int 4 d x = 4 x

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

Füge eine Konstante zur Lösung hinzu

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

Graph

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\int - t^{\frac{3}{2}} d t

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