integral of 1/(sqrt(2x-3)+1)

Lösung

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

2 x - 3 + 1 - ln 2 x - 3 + 1 + C

Schritte zur Lösung

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

Wende U-Substitution an

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

Wende U-Substitution an

= \int \frac{v - 1}{v} d v

Multipliziere aus

\frac{v - 1}{v} : 1 - \frac{1}{v}

= \int 1 - \frac{1}{v} d v

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 v - \int \frac{1}{v} d v

\int 1 d v = v

\int \frac{1}{v} d v = ln ∣ v ∣

= v - ln ∣ v ∣

Ersetze zurück

= 2 x - 3 + 1 - ln 2 x - 3 + 1

Füge eine Konstante zur Lösung hinzu

= 2 x - 3 + 1 - ln 2 x - 3 + 1 + C

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