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Beliebt Rechnen >

integral of (3/(x^5)-2/(x^2)-6/x)

Lösung

\int (\frac{3}{x ^{5}} - \frac{2}{x ^{2}} - \frac{6}{x}) d x

Lösung

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

Schritte zur Lösung

\int \frac{3}{x ^{5}} - \frac{2}{x ^{2}} - \frac{6}{x} 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{3}{x ^{5}} d x - \int \frac{2}{x ^{2}} d x - \int \frac{6}{x} d x

\int \frac{3}{x ^{5}} d x = - \frac{3}{4 x ^{4}}

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

\int \frac{6}{x} d x = 6 ln ∣ x ∣

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

Graph

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