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Beliebt Rechnen >

integral of-2x^3y^{-3}-x^2y^{-2}

Lösung

\int - 2 x^{3} y^{- 3} - x^{2} y^{- 2} d y

Lösung

\frac{x ^{2}}{y} + \frac{x ^{3}}{y ^{2}} + C

Schritte zur Lösung

\int - 2 x^{3} y^{- 3} - x^{2} y^{- 2} d y

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int x^{2} y^{- 2} d y - \int 2 x^{3} y^{- 3} d y

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

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

= - (- \frac{x ^{2}}{y}) - (- \frac{x ^{3}}{y ^{2}})

Vereinfache

= \frac{x ^{2}}{y} + \frac{x ^{3}}{y ^{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{2}}{y} + \frac{x ^{3}}{y ^{2}} + C

Graph

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