integral of x/(x-2)

Lösung

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

x - 2 + 2 ln ∣ x - 2 ∣ + C

Schritte zur Lösung

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

Wende U-Substitution an

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

Multipliziere aus

\frac{u + 2}{u} : 1 + \frac{2}{u}

= \int 1 + \frac{2}{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

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

\int 1 d u = u

\int \frac{2}{u} d u = 2 ln ∣ u ∣

= u + 2 ln ∣ u ∣

Setze in

u = x - 2

ein

= x - 2 + 2 ln ∣ x - 2 ∣

Füge eine Konstante zur Lösung hinzu

= x - 2 + 2 ln ∣ x - 2 ∣ + C

y^{^{'}} = \frac{x - 2}{y + 1}

\int - ∣ x ∣^{2} d x

\int_{0}^{1} 4 ln (x) d x

s l o p e \frac{d}{d x} (\frac{5}{4 x}) - \frac{7}{4}

\int \frac{( arctan ( x ) ) ^{3}}{1 + x ^{2}} d x