integral from 0 to ln(2) of tanh(2x)

Lösung

\int_{0}^{l n (2)} tanh (2 x) d x

\frac{1}{2} ln (\frac{17}{8})

Dezimale

0.37688 \dots

Schritte zur Lösung

\int_{0}^{l n (2)} tanh (2 x) d x

Wende U-Substitution an

= \int_{0}^{2 l n (2)} tanh (u) \frac{1}{2} d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int_{0}^{2 l n (2)} tanh (u) d u

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \frac{1}{2} \cdot \int_{0}^{2 l n (2)} \frac{sinh ( u )}{cosh ( u )} d u

Wende U-Substitution an

= \frac{1}{2} \cdot \int_{1}^{\frac{17}{8}} \frac{1}{v} d v

Nutze das gemeinsame Integral :

\int \frac{1}{v} d v = ln (∣ v ∣)

= \frac{1}{2} [ln ∣ v ∣]_{1}^{\frac{17}{8}}

Berechne die Grenzen:

ln (\frac{17}{8})

= \frac{1}{2} ln (\frac{17}{8})

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