integral from ln(2) to ln(10) of tanh(x)

Lösung

\int_{l n (2)}^{l n (10)} tanh (x) d x

ln (\frac{101}{25})

Dezimale

1.39624 \dots

Schritte zur Lösung

\int_{l n (2)}^{l n (10)} tanh (x) d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int_{l n (2)}^{l n (10)} \frac{sinh ( x )}{cosh ( x )} d x

Wende U-Substitution an

= \int_{\frac{5}{4}}^{\frac{101}{20}} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{\frac{5}{4}}^{\frac{101}{20}}

Berechne die Grenzen:

ln (\frac{101}{20}) - ln (\frac{5}{4})

= ln (\frac{101}{20}) - ln (\frac{5}{4})

Vereinfache

= ln (\frac{101}{25})

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