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Beliebt Rechnen >

integral of u^{-2}(2u^4+3u^2-2u^{-3})

Lösung

\int u^{- 2} (2 u^{4} + 3 u^{2} - 2 u^{- 3}) d u

Lösung

- \frac{2 u ^{7} + 3 u ^{5} - 2}{u ^{4}} + \frac{8 u ^{3}}{3} + 6 u - \frac{3}{2 u ^{4}} + C

Schritte zur Lösung

\int u^{- 2} (2 u^{4} + 3 u^{2} - 2 u^{- 3}) d u

Wende die partielle Integration an

= - \frac{2 u ^{7} + 3 u ^{5} - 2}{u ^{4}} - \int - \frac{8 u ^{7} + 6 u ^{5} + 6}{u ^{5}} d u

\int - \frac{8 u ^{7} + 6 u ^{5} + 6}{u ^{5}} d u = - \frac{8 u ^{3}}{3} - 6 u + \frac{3}{2 u ^{4}}

= - \frac{2 u ^{7} + 3 u ^{5} - 2}{u ^{4}} - (- \frac{8 u ^{3}}{3} - 6 u + \frac{3}{2 u ^{4}})

Vereinfache

= - \frac{2 u ^{7} + 3 u ^{5} - 2}{u ^{4}} + \frac{8 u ^{3}}{3} + 6 u - \frac{3}{2 u ^{4}}

Füge eine Konstante zur Lösung hinzu

= - \frac{2 u ^{7} + 3 u ^{5} - 2}{u ^{4}} + \frac{8 u ^{3}}{3} + 6 u - \frac{3}{2 u ^{4}} + C

Graph

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