de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of t/(t-2)

Lösung

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

Lösung

t - 2 + 2 ln ∣ t - 2 ∣ + C

Schritte zur Lösung

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

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 = t - 2

ein

= t - 2 + 2 ln ∣ t - 2 ∣

Füge eine Konstante zur Lösung hinzu

= t - 2 + 2 ln ∣ t - 2 ∣ + C

Graph

Beliebte Beispiele

integral of 1/(x-c)

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

integral of (x^4-2x^2+1)/(x^3)

\int \frac{x ^{4} - 2 x ^{2} + 1}{x ^{3}} d x

limit as x approaches 1-of 4x-5

x \to 1 - lim (4 x - 5)

derivative 2/(3x)

d er i v a t i v e \frac{2}{3 x}

integral of-(12)/(x^{13)}

\int - \frac{12}{x ^{13}} d x