integral from 3 to 4 of 1/x log_{e}(x)

Lösung

\int_{3}^{4} \frac{1}{x} lo g_{e} (x) d x

2 ln^{2} (2) - \frac{ln ^{2} ( 3 )}{2}

Dezimale

0.35743 \dots

Schritte zur Lösung

\int_{3}^{4} \frac{1}{x} lo g_{e} (x) d x

Vereinfache

\frac{1}{x} lo g_{e} (x) : \frac{ln ( x )}{x}

= \int_{3}^{4} \frac{ln ( x )}{x} d x

Wende U-Substitution an

= \int_{l n (3)}^{2 l n (2)} u d u

Wende die Potenzregel an

= [\frac{u ^{2}}{2}]_{l n (3)}^{2 l n (2)}

Berechne die Grenzen:

2 ln^{2} (2) - \frac{ln ^{2} ( 3 )}{2}

= 2 ln^{2} (2) - \frac{ln ^{2} ( 3 )}{2}

\int_{3}^{5} \frac{( x + 2 ) ^{2}}{x - 2} d x

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