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Beliebt Rechnen >

integral of 2/x-3/(x^4)

Lösung

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

Lösung

2 ln ∣ x ∣ + \frac{1}{x ^{3}} + C

Schritte zur Lösung

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

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

= 2 ln ∣ x ∣ - (- \frac{1}{x ^{3}})

Vereinfache

= 2 ln ∣ x ∣ + \frac{1}{x ^{3}}

Füge eine Konstante zur Lösung hinzu

= 2 ln ∣ x ∣ + \frac{1}{x ^{3}} + C

Graph

Beliebte Beispiele

derivative of y+3y=0

\frac{d}{d x} y + 3 y = 0

steigung (5,-3),(-1,-1)

s l o p e (5, - 3), (- 1, - 1)

limit as x approaches 0 of (x-45)/(x-5)

x \to 0 lim (\frac{x - 45}{x - 5})

y^{^{'}} = t y^{3}

limit as x approaches 8 of cos(1/(x-8))

x \to 8 lim (cos (\frac{1}{x - 8}))