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Beliebt Rechnen >

integral of (6s^2-2)/(s^3)

Lösung

\int \frac{6 s ^{2} - 2}{s ^{3}} d s

Lösung

6 ln ∣ s ∣ + \frac{1}{s ^{2}} + C

Schritte zur Lösung

\int \frac{6 s ^{2} - 2}{s ^{3}} d s

Multipliziere aus

\frac{6 s ^{2} - 2}{s ^{3}} : \frac{6}{s} - \frac{2}{s ^{3}}

= \int \frac{6}{s} - \frac{2}{s ^{3}} d s

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{6}{s} d s - \int \frac{2}{s ^{3}} d s

\int \frac{6}{s} d s = 6 ln ∣ s ∣

\int \frac{2}{s ^{3}} d s = - \frac{1}{s ^{2}}

= 6 ln ∣ s ∣ - (- \frac{1}{s ^{2}})

Vereinfache

= 6 ln ∣ s ∣ + \frac{1}{s ^{2}}

Füge eine Konstante zur Lösung hinzu

= 6 ln ∣ s ∣ + \frac{1}{s ^{2}} + C

Graph

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