integral from 1 to 4 of (ln(x))/(x^3)

Lösung

\int_{1}^{4} \frac{ln ( x )}{x ^{3}} d x

\frac{15}{64} - \frac{1}{16} ln (2)

Dezimale

0.19105 \dots

Schritte zur Lösung

\int_{1}^{4} \frac{ln ( x )}{x ^{3}} d x

Wende die partielle Integration an

= [- \frac{ln ( x )}{2 x ^{2}} - \int - \frac{1}{2 x ^{3}} d x]_{1}^{4}

\int - \frac{1}{2 x ^{3}} d x = \frac{1}{4 x ^{2}}

= [- \frac{ln ( x )}{2 x ^{2}} - \frac{1}{4 x ^{2}}]_{1}^{4}

Berechne die Grenzen:

\frac{15}{64} - \frac{1}{16} ln (2)

= \frac{15}{64} - \frac{1}{16} ln (2)

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