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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 + arctan (x) + 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 = arctan (x)

= \frac{x ^{3}}{3} - x + arctan (x)

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{3}}{3} - x + arctan (x) + C

Graph

Beliebte Beispiele

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\int 3 x^{2} - x + 1 d x

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