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

Lösung

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

ln (\frac{5}{4})

Dezimale

0.22314 \dots

Schritte zur Lösung

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

Umschreiben mit Hilfe von Trigonometrie-Identitäten

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

Wende U-Substitution an

= \int_{1}^{\frac{5}{4}} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{1}^{\frac{5}{4}}

Berechne die Grenzen:

ln (\frac{5}{4})

= ln (\frac{5}{4})

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