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Beliebt Rechnen >

integral of (8t-5)/(t+1)

Lösung

\int \frac{8 t - 5}{t + 1} d t

Lösung

8 (t + 1) - 13 ln ∣ t + 1 ∣ + C

Schritte zur Lösung

\int \frac{8 t - 5}{t + 1} d t

Wende U-Substitution an

= \int \frac{8 u - 13}{u} d u

Multipliziere aus

\frac{8 u - 13}{u} : 8 - \frac{13}{u}

= \int 8 - \frac{13}{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 8 d u - \int \frac{13}{u} d u

\int 8 d u = 8 u

\int \frac{13}{u} d u = 13 ln ∣ u ∣

= 8 u - 13 ln ∣ u ∣

Setze in

u = t + 1

ein

= 8 (t + 1) - 13 ln ∣ t + 1 ∣

Füge eine Konstante zur Lösung hinzu

= 8 (t + 1) - 13 ln ∣ t + 1 ∣ + C

Graph

Beliebte Beispiele

integral of 24x^3

\int 24 x^{3} d x

limit as x approaches 2 of (x-2)/(2-x)

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

derivative 2/(t+1)

d er i v a t i v e \frac{2}{t + 1}

derivative 46-x/(250)

d er i v a t i v e 46 - \frac{x}{250}

derivative (12)/(x^2(x-3))

d er i v a t i v e \frac{12}{x ^{2} ( x - 3 )}