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Beliebt Rechnen >

integral of u^{-5}(7-u^5+u^{10})

Lösung

\int u^{- 5} (7 - u^{5} + u^{10}) d u

Lösung

- \frac{7}{4 u ^{4}} - u + \frac{u ^{6}}{6} + C

Schritte zur Lösung

\int u^{- 5} (7 - u^{5} + u^{10}) d u

Multipliziere aus

u^{- 5} (7 - u^{5} + u^{10}) : \frac{7}{u ^{5}} - 1 + u^{5}

= \int \frac{7}{u ^{5}} - 1 + u^{5} d u

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{7}{u ^{5}} d u - \int 1 d u + \int u^{5} d u

\int \frac{7}{u ^{5}} d u = - \frac{7}{4 u ^{4}}

\int 1 d u = u

\int u^{5} d u = \frac{u ^{6}}{6}

= - \frac{7}{4 u ^{4}} - u + \frac{u ^{6}}{6}

Füge eine Konstante zur Lösung hinzu

= - \frac{7}{4 u ^{4}} - u + \frac{u ^{6}}{6} + C

Graph

Beliebte Beispiele

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integral of 5x^{3/2}+2sqrt(x)

\int 5 x^{\frac{3}{2}} + 2 x d x