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Beliebt Rechnen >

integral of (s^2-4s-6)/(s^4)

Lösung

\int \frac{s ^{2} - 4 s - 6}{s ^{4}} d s

Lösung

- \frac{1}{s} + \frac{2}{s ^{2}} + \frac{2}{s ^{3}} + C

Schritte zur Lösung

\int \frac{s ^{2} - 4 s - 6}{s ^{4}} d s

Multipliziere aus

\frac{s ^{2} - 4 s - 6}{s ^{4}} : \frac{1}{s ^{2}} - \frac{4}{s ^{3}} - \frac{6}{s ^{4}}

= \int \frac{1}{s ^{2}} - \frac{4}{s ^{3}} - \frac{6}{s ^{4}} 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{1}{s ^{2}} d s - \int \frac{4}{s ^{3}} d s - \int \frac{6}{s ^{4}} d s

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

\int \frac{4}{s ^{3}} d s = - \frac{2}{s ^{2}}

\int \frac{6}{s ^{4}} d s = - \frac{2}{s ^{3}}

= - \frac{1}{s} - (- \frac{2}{s ^{2}}) - (- \frac{2}{s ^{3}})

Vereinfache

= - \frac{1}{s} + \frac{2}{s ^{2}} + \frac{2}{s ^{3}}

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{s} + \frac{2}{s ^{2}} + \frac{2}{s ^{3}} + C

Graph

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