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Beliebt Rechnen >

integral of (7x^2-2)/(x^2)

Lösung

\int \frac{7 x ^{2} - 2}{x ^{2}} d x

Lösung

7 x + \frac{2}{x} + C

Schritte zur Lösung

\int \frac{7 x ^{2} - 2}{x ^{2}} d x

Multipliziere aus

\frac{7 x ^{2} - 2}{x ^{2}} : 7 - \frac{2}{x ^{2}}

= \int 7 - \frac{2}{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 7 d x - \int \frac{2}{x ^{2}} d x

\int 7 d x = 7 x

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

= 7 x - (- \frac{2}{x})

Vereinfache

= 7 x + \frac{2}{x}

Füge eine Konstante zur Lösung hinzu

= 7 x + \frac{2}{x} + C

Graph

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