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Beliebt Rechnen >

integral of x^3(2-x^2)

Lösung

\int x^{3} (2 - x^{2}) d x

Lösung

\frac{1}{4} x^{4} (2 - x^{2}) + \frac{x ^{6}}{12} + C

Schritte zur Lösung

\int x^{3} (2 - x^{2}) d x

Wende die partielle Integration an

= \frac{1}{4} x^{4} (2 - x^{2}) - \int - \frac{x ^{5}}{2} d x

\int - \frac{x ^{5}}{2} d x = - \frac{x ^{6}}{12}

= \frac{1}{4} x^{4} (2 - x^{2}) - (- \frac{x ^{6}}{12})

Vereinfache

= \frac{1}{4} x^{4} (2 - x^{2}) + \frac{x ^{6}}{12}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{4} x^{4} (2 - x^{2}) + \frac{x ^{6}}{12} + C

Graph

Beliebte Beispiele

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\int \frac{x ^{2}}{10 x - x ^{2}} d x

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\int (\frac{x ^{3} + 2 x - 7}{x}) d x

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\int (cos (x) + \frac{1}{x} + π x) d x

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

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