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Beliebt Rechnen >

integral of (x^4)/2-x+2/(x^3)

Lösung

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

Lösung

\frac{x ^{5}}{10} - \frac{x ^{2}}{2} - \frac{1}{x ^{2}} + C

Schritte zur Lösung

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

\int \frac{x ^{4}}{2} d x = \frac{x ^{5}}{10}

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

\int \frac{2}{x ^{3}} d x = - \frac{1}{x ^{2}}

= \frac{x ^{5}}{10} - \frac{x ^{2}}{2} - \frac{1}{x ^{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{5}}{10} - \frac{x ^{2}}{2} - \frac{1}{x ^{2}} + C

Graph

Beliebte Beispiele

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\int \frac{1}{( x ^{2} + 49 ) ^{2}} d x

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\int arcsec (5 x) d x

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\int \frac{- y ^{2}}{2} d y

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\int (sin (x))^{7} (cos (x))^{4} d x