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Beliebt Rechnen >

integral of (2/(x^5)+1/x)

Lösung

\int (\frac{2}{x ^{5}} + \frac{1}{x}) d x

Lösung

- \frac{1}{2 x ^{4}} + ln ∣ x ∣ + C

Schritte zur Lösung

\int \frac{2}{x ^{5}} + \frac{1}{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{2}{x ^{5}} d x + \int \frac{1}{x} d x

\int \frac{2}{x ^{5}} d x = - \frac{1}{2 x ^{4}}

\int \frac{1}{x} d x = ln ∣ x ∣

= - \frac{1}{2 x ^{4}} + ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{2 x ^{4}} + ln ∣ x ∣ + C

Graph

Beliebte Beispiele

integral of (4x^2)/(sqrt(1-12x^3))

\int \frac{4 x ^{2}}{1 - 12 x ^{3}} d x

integral of 1/(y^2+x^2)

\int \frac{1}{y ^{2} + x ^{2}} d x

integral of tan(5x-1)

\int tan (5 x - 1) d x

integral of 3xsqrt(x^2-5)

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

integral of e^{-it}

\int e^{- i t} d t