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Beliebt Rechnen >

integral of (4x^2+8x-18)/(x^4)

Lösung

\int \frac{4 x ^{2} + 8 x - 18}{x ^{4}} d x

Lösung

- \frac{4}{x} - \frac{4}{x ^{2}} + \frac{6}{x ^{3}} + C

Schritte zur Lösung

\int \frac{4 x ^{2} + 8 x - 18}{x ^{4}} d x

Multipliziere aus

\frac{4 x ^{2} + 8 x - 18}{x ^{4}} : \frac{4}{x ^{2}} + \frac{8}{x ^{3}} - \frac{18}{x ^{4}}

= \int \frac{4}{x ^{2}} + \frac{8}{x ^{3}} - \frac{18}{x ^{4}} 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{8}{x ^{3}} d x - \int \frac{18}{x ^{4}} d x

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

\int \frac{8}{x ^{3}} d x = - \frac{4}{x ^{2}}

\int \frac{18}{x ^{4}} d x = - \frac{6}{x ^{3}}

= - \frac{4}{x} - \frac{4}{x ^{2}} - (- \frac{6}{x ^{3}})

Vereinfache

= - \frac{4}{x} - \frac{4}{x ^{2}} + \frac{6}{x ^{3}}

Füge eine Konstante zur Lösung hinzu

= - \frac{4}{x} - \frac{4}{x ^{2}} + \frac{6}{x ^{3}} + C

Graph

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