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Beliebt Rechnen >

integral of ((x^5-x^3+4x))/(x^4)

Lösung

\int \frac{( x ^{5} - x ^{3} + 4 x )}{x ^{4}} d x

Lösung

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

Schritte zur Lösung

\int \frac{x ^{5} - x ^{3} + 4 x}{x ^{4}} d x

Multipliziere aus

\frac{x ^{5} - x ^{3} + 4 x}{x ^{4}} : x - \frac{1}{x} + \frac{4}{x ^{3}}

= \int x - \frac{1}{x} + \frac{4}{x ^{3}} 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{1}{x} d x + \int \frac{4}{x ^{3}} d x

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

\int \frac{1}{x} d x = ln ∣ x ∣

\int \frac{4}{x ^{3}} d x = - \frac{2}{x ^{2}}

= \frac{x ^{2}}{2} - ln ∣ x ∣ - \frac{2}{x ^{2}}

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

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\int x e^{x^{2}} sin (a x^{2}) d x

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\int x^{3} x^{2} + 21 d x

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\int \frac{3 x ^{2} + 1}{x ^{2} ( 1 + x ^{2} )} d x

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\int \frac{2}{x ^{2} ( x ^{2} - 4 x - 5 )} d x