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Beliebt Rechnen >

integral of (x^5+x-1)/(x^3+1)

Lösung

\int \frac{x ^{5} + x - 1}{x ^{3} + 1} d x

Lösung

\frac{x ^{3}}{3} - ln ∣ x + 1 ∣ + C

Schritte zur Lösung

\int \frac{x ^{5} + x - 1}{x ^{3} + 1} d x

Lange Division

\frac{x ^{5} + x - 1}{x ^{3} + 1} : x^{2} - \frac{1}{x + 1}

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

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

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

= \frac{x ^{3}}{3} - ln ∣ x + 1 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{3}}{3} - ln ∣ x + 1 ∣ + C

Graph

Beliebte Beispiele

inverselaplace 2/(s^2-s)

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

fläche 8cos(4x),8-8cos(4x),0, pi/4

a re a 8 cos (4 x), 8 - 8 cos (4 x), 0, \frac{π}{4}

derivative of (2x/(2+sqrt(x)))

\frac{d}{d x} (\frac{2 x}{2 + x})

integral of xcos(3pix^2)

\int x cos (3 π x^{2}) d x

ln (x) y^{^{'}} = \frac{y}{x}