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

Lösung

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

Ci (e) - 0.03434 \dots

Schritte zur Lösung

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

Wende die partielle Integration an

= [- ln (x) cos (x) - \int - \frac{cos ( x )}{x} d x]_{1}^{e}

\int - \frac{cos ( x )}{x} d x = - Ci (x)

= [- ln (x) cos (x) - (- Ci (x))]_{1}^{e}

Vereinfache

= [- ln (x) cos (x) + Ci (x)]_{1}^{e}

Berechne die Grenzen:

- cos (e) + Ci (e) - 0.9460830704

= - cos (e) + Ci (e) - 0.94608 \dots

Vereinfache

= Ci (e) - 0.03434 \dots

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