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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

Graph

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