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Beliebt Rechnen >

integral of (x^2-4)/(x-2)

Lösung

\int \frac{x ^{2} - 4}{x - 2} d x

Lösung

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

Schritte zur Lösung

\int \frac{x ^{2} - 4}{x - 2} d x

Vereinfache

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

= \int x + 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 d x + \int 2 d x

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

\int 2 d x = 2 x

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

f(x)=(3x^2+2)^2(x^2-5x)^3

f (x) = (3 x^{2} + 2)^{2} (x^{2} - 5 x)^{3}

integral of x^2ln(x^3)

\int x^{2} ln (x^{3}) d x

limit as x approaches-1-of x^3+2x^2+1

x \to - 1 - lim (x^{3} + 2 x^{2} + 1)

integral of x^4ln(5x)

\int x^{4} ln (5 x) d x

(ln (x^{3}))^{^{'}}