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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

Beliebte Beispiele

integral of (x+ln(x^2))/x

\int \frac{x + ln ( x ^{2} )}{x} d x

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integral of (10)/(xln(x))

\int \frac{10}{x ln ( x )} d x

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\int 2 x ln (x - 1) d x

integral of (20)/(sqrt(1-x^2))

\int \frac{20}{1 - x ^{2}} d x