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Beliebt Rechnen >

integral of (x+2)/(x-1)

Lösung

\int \frac{x + 2}{x - 1} d x

Lösung

x - 1 + 3 ln ∣ x - 1 ∣ + C

Schritte zur Lösung

\int \frac{x + 2}{x - 1} d x

Multipliziere aus

\frac{x + 2}{x - 1} : \frac{x}{x - 1} + \frac{2}{x - 1}

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{x}{x - 1} d x + \int \frac{2}{x - 1} d x

\int \frac{x}{x - 1} d x = x - 1 + ln ∣ x - 1 ∣

\int \frac{2}{x - 1} d x = 2 ln ∣ x - 1 ∣

= x - 1 + ln ∣ x - 1 ∣ + 2 ln ∣ x - 1 ∣

Vereinfache

= x - 1 + 3 ln ∣ x - 1 ∣

Füge eine Konstante zur Lösung hinzu

= x - 1 + 3 ln ∣ x - 1 ∣ + C

Graph

Beliebte Beispiele

tangent f(x)=sqrt(7x+2),\at x=2

t an g e n t f (x) = 7 x + 2, at x = 2

(21+x^2)y^'-2xy=0

(21 + x^{2}) y^{^{'}} - 2 x y = 0

y^'=9.8-(3y)/(3.5)

y^{^{'}} = 9.8 - \frac{3 y}{3.5}

limit as x approaches infinity of (n^{1.5})/(ln(n))

x \to \infty lim (\frac{n ^{1.5}}{ln ( n )})

(6+x)((dy)/(dx))=9y

(6 + x) (\frac{d y}{d x}) = 9 y