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Beliebt Rechnen >

integral of u^{-3}(4-u^3+u^6)

Lösung

\int u^{- 3} (4 - u^{3} + u^{6}) d u

Lösung

- \frac{2}{u ^{2}} - u + \frac{u ^{4}}{4} + C

Schritte zur Lösung

\int u^{- 3} (4 - u^{3} + u^{6}) d u

Multipliziere aus

u^{- 3} (4 - u^{3} + u^{6}) : \frac{4}{u ^{3}} - 1 + u^{3}

= \int \frac{4}{u ^{3}} - 1 + u^{3} 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{4}{u ^{3}} d u - \int 1 d u + \int u^{3} d u

\int \frac{4}{u ^{3}} d u = - \frac{2}{u ^{2}}

\int 1 d u = u

\int u^{3} d u = \frac{u ^{4}}{4}

= - \frac{2}{u ^{2}} - u + \frac{u ^{4}}{4}

Füge eine Konstante zur Lösung hinzu

= - \frac{2}{u ^{2}} - u + \frac{u ^{4}}{4} + C

Graph

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