integral from ln(2) to ln(4) of (e^{-x})/(sqrt(1-e^{-2x))}

Lösung

\int_{l n (2)}^{l n (4)} \frac{e ^{- x}}{1 - e ^{- 2 x}} d x

arcsin (\frac{15}{4}) - \frac{π}{3}

Dezimale

0.27091 \dots

Schritte zur Lösung

\int_{l n (2)}^{l n (4)} \frac{e ^{- x}}{1 - e ^{- 2 x}} d x

Wende U-Substitution an

= \int_{\frac{3}{2}}^{\frac{15}{4}} \frac{1}{- u ^{2} + 1} d u

Nutze das gemeinsame Integral :

\int \frac{1}{- u ^{2} + 1} d u = arcsin (u)

= [arcsin (u)]_{\frac{3}{2}}^{\frac{15}{4}}

Berechne die Grenzen:

arcsin (\frac{15}{4}) - \frac{π}{3}

= arcsin (\frac{15}{4}) - \frac{π}{3}

\int_{1}^{3} (x + 1) e^{x^{2} + 2 x} d x

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\int_{0}^{\frac{π}{4}} x cos (x) d x

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\int_{1}^{e^{x}} \frac{x}{y} d y