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Beliebt Rechnen >

integral of (7t-6)/(t+1)

Lösung

\int \frac{7 t - 6}{t + 1} d t

Lösung

7 (t + 1) - 13 ln ∣ t + 1 ∣ + C

Schritte zur Lösung

\int \frac{7 t - 6}{t + 1} d t

Wende U-Substitution an

= \int \frac{7 u - 13}{u} d u

Multipliziere aus

\frac{7 u - 13}{u} : 7 - \frac{13}{u}

= \int 7 - \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 7 d u - \int \frac{13}{u} d u

\int 7 d u = 7 u

\int \frac{13}{u} d u = 13 ln ∣ u ∣

= 7 u - 13 ln ∣ u ∣

Setze in

u = t + 1

ein

= 7 (t + 1) - 13 ln ∣ t + 1 ∣

Füge eine Konstante zur Lösung hinzu

= 7 (t + 1) - 13 ln ∣ t + 1 ∣ + C

Graph

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