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Beliebt Rechnen >

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

Lösung

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

Lösung

3 ln ∣ x ∣ + \frac{1}{x ^{5}} + C

Schritte zur Lösung

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

\int \frac{3}{x} d x = 3 ln ∣ x ∣

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

= 3 ln ∣ x ∣ - (- \frac{1}{x ^{5}})

Vereinfache

= 3 ln ∣ x ∣ + \frac{1}{x ^{5}}

Füge eine Konstante zur Lösung hinzu

= 3 ln ∣ x ∣ + \frac{1}{x ^{5}} + C

Graph

Beliebte Beispiele

(dy}{dx}=\frac{x^3-x^2+x)/x

\frac{d y}{d x} = \frac{x ^{3} - x ^{2} + x}{x}

tangent y=tan(x)+1/3 tan^3(x)

t an g e n t y = tan (x) + \frac{1}{3} tan^{3} (x)

limit as x approaches-3 of x^3+4x^2-7

x \to - 3 lim (x^{3} + 4 x^{2} - 7)

y^{''}+4y=e^{-x}(7-4x+5x^2)

y^{^{''}} + 4 y = e^{- x} (7 - 4 x + 5 x^{2})

(dy)/(dx)=(y+1)(y-2),y(0)=0

\frac{d y}{d x} = (y + 1) (y - 2), y (0) = 0