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Beliebt Rechnen >

integral of 4x^{-2}+3x^{-1}-1

Lösung

\int 4 x^{- 2} + 3 x^{- 1} - 1 d x

Lösung

- \frac{4}{x} + 3 ln ∣ x ∣ - x + C

Schritte zur Lösung

\int 4 x^{- 2} + 3 x^{- 1} - 1 d x

Vereinfache

4 x^{- 2} + 3 x^{- 1} - 1 : \frac{4}{x ^{2}} + \frac{3}{x} - 1

= \int \frac{4}{x ^{2}} + \frac{3}{x} - 1 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 \frac{4}{x ^{2}} d x + \int \frac{3}{x} d x - \int 1 d x

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

\int \frac{3}{x} d x = 3 ln ∣ x ∣

\int 1 d x = x

= - \frac{4}{x} + 3 ln ∣ x ∣ - x

Füge eine Konstante zur Lösung hinzu

= - \frac{4}{x} + 3 ln ∣ x ∣ - x + C

Graph

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