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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{4 x ^{3}}{3} - \frac{3}{x} + C

Schritte zur Lösung

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

3 x^{- 2} = \frac{3}{x ^{2}}

= \int 4 x^{2} + \frac{3}{x ^{2}} d x

Wende die Summenregel an:

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

= \int 4 x^{2} d x + \int \frac{3}{x ^{2}} d x

\int 4 x^{2} d x = \frac{4 x ^{3}}{3}

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

= \frac{4 x ^{3}}{3} - \frac{3}{x}

Füge eine Konstante zur Lösung hinzu

= \frac{4 x ^{3}}{3} - \frac{3}{x} + C

Graph

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