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Beliebt Rechnen >

integral of (x^4)/(x^2-1)

Lösung

\int \frac{x ^{4}}{x ^{2} - 1} d x

Lösung

\frac{x ^{3}}{3} + x - \frac{1}{2} ln ∣ x + 1 ∣ + \frac{1}{2} ln ∣ x - 1 ∣ + C

Schritte zur Lösung

\int \frac{x ^{4}}{x ^{2} - 1} d x

Lange Division

\frac{x ^{4}}{x ^{2} - 1} : x^{2} + 1 + \frac{1}{x ^{2} - 1}

= \int x^{2} + 1 + \frac{1}{x ^{2} - 1} 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 1 d x + \int \frac{1}{x ^{2} - 1} d x

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

\int 1 d x = x

\int \frac{1}{x ^{2} - 1} d x = - \frac{1}{2} ln ∣ x + 1 ∣ + \frac{1}{2} ln ∣ x - 1 ∣

= \frac{x ^{3}}{3} + x - \frac{1}{2} ln ∣ x + 1 ∣ + \frac{1}{2} ln ∣ x - 1 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{3}}{3} + x - \frac{1}{2} ln ∣ x + 1 ∣ + \frac{1}{2} ln ∣ x - 1 ∣ + C

Graph

Beliebte Beispiele

integral of xcos(xn)

\int x cos (x n) d x

integral of sqrt(x)(6-x)

\int x (6 - x) d x

inverselaplace s/((s^2-k^2))

in v erse l a pl a ce \frac{s}{( s ^{2} - k ^{2} )}

(\partial)/(\partial x)((x^3)sqrt(x^2+9))

\frac{\partial}{\partial x} ((x^{3}) x^{2} + 9)

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

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