integral of (7/x-5/(x^6))

Lösung

\int (\frac{7}{x} - \frac{5}{x ^{6}}) d x

7 ln ∣ x ∣ + \frac{1}{x ^{5}} + C

Schritte zur Lösung

\int \frac{7}{x} - \frac{5}{x ^{6}} 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{7}{x} d x - \int \frac{5}{x ^{6}} d x

\int \frac{7}{x} d x = 7 ln ∣ x ∣

\int \frac{5}{x ^{6}} d x = - \frac{1}{x ^{5}}

= 7 ln ∣ x ∣ - (- \frac{1}{x ^{5}})

Vereinfache

= 7 ln ∣ x ∣ + \frac{1}{x ^{5}}

Füge eine Konstante zur Lösung hinzu

= 7 ln ∣ x ∣ + \frac{1}{x ^{5}} + C

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