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Beliebt Rechnen >

integral of (x^2+48x-16)/(x^3-16x)

Lösung

\int \frac{x ^{2} + 48 x - 16}{x ^{3} - 16 x} d x

Lösung

ln ∣ x ∣ - 6 ln ∣ x + 4 ∣ + 6 ln ∣ x - 4 ∣ + C

Schritte zur Lösung

\int \frac{x ^{2} + 48 x - 16}{x ^{3} - 16 x} d x

Ermittle den Partialbruch von

\frac{x ^{2} + 48 x - 16}{x ^{3} - 16 x} : \frac{1}{x} - \frac{6}{x + 4} + \frac{6}{x - 4}

= \int \frac{1}{x} - \frac{6}{x + 4} + \frac{6}{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 \frac{1}{x} d x - \int \frac{6}{x + 4} d x + \int \frac{6}{x - 4} d x

\int \frac{1}{x} d x = ln ∣ x ∣

\int \frac{6}{x + 4} d x = 6 ln ∣ x + 4 ∣

\int \frac{6}{x - 4} d x = 6 ln ∣ x - 4 ∣

= ln ∣ x ∣ - 6 ln ∣ x + 4 ∣ + 6 ln ∣ x - 4 ∣

Füge eine Konstante zur Lösung hinzu

= ln ∣ x ∣ - 6 ln ∣ x + 4 ∣ + 6 ln ∣ x - 4 ∣ + C

Graph

Beliebte Beispiele

derivative of 2^x+1

(dy)/(dt)=-y/(t^2)

tangent f(x)=6x-x^2,\at x=4

derivative of (x-5sin(x))

sum from n=0 to infinity of 1/(1.5^n)