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Beliebt Rechnen >

integral of (x^2+1)(x^2-1)

Lösung

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

Lösung

\frac{x ^{5}}{5} - x + C

Schritte zur Lösung

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

Multipliziere mit der Konjugation von

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

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

Vereinfache

\frac{x ^{4} - 1}{x ^{2} - 1} (x^{2} - 1) : x^{4} - 1

= \int x^{4} - 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^{4} d x - \int 1 d x

\int x^{4} d x = \frac{x ^{5}}{5}

\int 1 d x = x

= \frac{x ^{5}}{5} - x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{5}}{5} - x + C

Graph

Beliebte Beispiele

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\int \frac{3}{u ^{2}} d u

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\int \frac{x ^{5} + 3 x}{x ^{4} + 1} d x