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Beliebt Rechnen >

integral of (9x^2-6)/(x^2)

Lösung

\int \frac{9 x ^{2} - 6}{x ^{2}} d x

Lösung

9 x + \frac{6}{x} + C

Schritte zur Lösung

\int \frac{9 x ^{2} - 6}{x ^{2}} d x

Multipliziere aus

\frac{9 x ^{2} - 6}{x ^{2}} : 9 - \frac{6}{x ^{2}}

= \int 9 - \frac{6}{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 9 d x - \int \frac{6}{x ^{2}} d x

\int 9 d x = 9 x

\int \frac{6}{x ^{2}} d x = - \frac{6}{x}

= 9 x - (- \frac{6}{x})

Vereinfache

= 9 x + \frac{6}{x}

Füge eine Konstante zur Lösung hinzu

= 9 x + \frac{6}{x} + C

Graph

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