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Beliebt Rechnen >

integral of 1/(sqrt(x)-1)

Lösung

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

Lösung

2 (x - 1 + ln x - 1) + C

Schritte zur Lösung

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

Wende U-Substitution an

= \int \frac{2 ( u + 1 )}{u} d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int \frac{u + 1}{u} d u

Multipliziere aus

\frac{u + 1}{u} : 1 + \frac{1}{u}

= 2 \cdot \int 1 + \frac{1}{u} d u

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 2 (\int 1 d u + \int \frac{1}{u} d u)

\int 1 d u = u

\int \frac{1}{u} d u = ln ∣ u ∣

= 2 (u + ln ∣ u ∣)

Setze in

u = x - 1

ein

= 2 (x - 1 + ln x - 1)

Füge eine Konstante zur Lösung hinzu

= 2 (x - 1 + ln x - 1) + C

Graph

Beliebte Beispiele

limit as x approaches 2 of 2-x^2

x \to 2 lim (2 - x^{2})

integral from 1 to e^4 of x^4ln(x)

\int_{1}^{e^{4}} x^{4} ln (x) d x

tangent f(x)=x^2-2x+5,\at x=1

t an g e n t f (x) = x^{2} - 2 x + 5, at x = 1

derivative sqrt(8+5x)

d er i v a t i v e 8 + 5 x

tangent y=x^2+4,(-5,29)

t an g e n t y = x^{2} + 4, (- 5, 29)