integral from 1 to e of (ln(9x))/x

Lösung

\int_{1}^{e} \frac{ln ( 9 x )}{x} d x

\frac{ln ^{2} ( 9 e )}{2} - 2 ln^{2} (3)

Dezimale

2.69722 \dots

Schritte zur Lösung

\int_{1}^{e} \frac{ln ( 9 x )}{x} d x

Wende U-Substitution an

= \int_{9}^{9 e} \frac{ln ( u )}{u} d u

Wende U-Substitution an

= \int_{2 l n (3)}^{l n (9 e)} v d v

Wende die Potenzregel an

= [\frac{v ^{2}}{2}]_{2 l n (3)}^{l n (9 e)}

Berechne die Grenzen:

\frac{ln ^{2} ( 9 e )}{2} - 2 ln^{2} (3)

= \frac{ln ^{2} ( 9 e )}{2} - 2 ln^{2} (3)

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