integral from 1 to e of (sin(ln(x)))/x

Lösung

\int_{1}^{e} \frac{sin ( ln ( x ) )}{x} d x

- cos (1) + 1

Dezimale

0.45969 \dots

Schritte zur Lösung

\int_{1}^{e} \frac{sin ( ln ( x ) )}{x} d x

Wende U-Substitution an

= \int_{0}^{1} sin (u) d u

Nutze das gemeinsame Integral :

\int sin (u) d u = - cos (u)

= [- cos (u)]_{0}^{1}

Berechne die Grenzen:

- cos (1) + 1

= - cos (1) + 1

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