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Beliebt Rechnen >

integral of ((y+1))/((y-1))

Lösung

\int \frac{( y + 1 )}{( y - 1 )} d y

Lösung

2 ln ∣ y - 1 ∣ + y + C

Schritte zur Lösung

\int \frac{y + 1}{y - 1} d y

\frac{y + 1}{y - 1} = \frac{2}{y - 1} + 1

= \int \frac{2}{y - 1} + 1 d y

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}{y - 1} d y + \int 1 d y

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

\int 1 d y = y

= 2 ln ∣ y - 1 ∣ + y

Füge eine Konstante zur Lösung hinzu

= 2 ln ∣ y - 1 ∣ + y + C

Graph

Beliebte Beispiele

integral of 6x^5-18x^2+7

\int 6 x^{5} - 18 x^{2} + 7 d x

dx=xsqrt(x^2-16)dy

d x = x x^{2} - 16 d y

limit as x approaches 20 of sqrt(10)

x \to 20 lim (10)

integral of ((4+x^7)^67x^6)

\int ((4 + x^{7})^{6} 7 x^{6}) d x

limit as x approaches 3 of 10

x \to 3 lim (10)