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Beliebt Rechnen >

integral of (x^2-4)/x

Lösung

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

Lösung

\frac{x ^{2}}{2} - 4 ln ∣ x ∣ + C

Schritte zur Lösung

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

Multipliziere aus

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

= \int x - \frac{4}{x} 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 \frac{4}{x} d x

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

\int \frac{4}{x} d x = 4 ln ∣ x ∣

= \frac{x ^{2}}{2} - 4 ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{2}}{2} - 4 ln ∣ x ∣ + C

Graph

Beliebte Beispiele

derivative of x^2sqrt(2x-3)

\frac{d}{d x} (x^{2} 2 x - 3)

x^2y^'+4/3 xy=-4cos(3x)y^{-1/2}

x^{2} y^{^{'}} + \frac{4}{3} x y = - 4 cos (3 x) y^{- \frac{1}{2}}

limit as x approaches 1+of 1/(x^2-1)

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

y^{''}-4y=0,y(0)=0,y^'(0)=1

y^{^{''}} - 4 y = 0, y (0) = 0, y^{^{'}} (0) = 1

tangent f(x)= 4/(1+x^2),(1,2)

t an g e n t f (x) = \frac{4}{1 + x ^{2}}, (1, 2)