integral from 1 to 10 of ((ln(x))/(ln(10)))

Lösung

\int_{1}^{10} (\frac{ln ( x )}{ln ( 10 )}) d x

\frac{10 ln ( 10 ) - 9}{ln ( 10 )}

Dezimale

6.09134 \dots

Schritte zur Lösung

\int_{1}^{10} \frac{ln ( x )}{ln ( 10 )} d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{ln ( 10 )} \cdot \int_{1}^{10} ln (x) d x

Wende die partielle Integration an

= \frac{1}{ln ( 10 )} [x ln (x) - \int 1 d x]_{1}^{10}

\int 1 d x = x

= \frac{1}{ln ( 10 )} [x ln (x) - x]_{1}^{10}

Berechne die Grenzen:

10 ln (10) - 9

= \frac{1}{ln ( 10 )} (10 ln (10) - 9)

Vereinfache

= \frac{10 ln ( 10 ) - 9}{ln ( 10 )}

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