integral from 1 to 5 of (ln(x^2))/(x^3)

Lösung

\int_{1}^{5} \frac{ln ( x ^{2} )}{x ^{3}} d x

\frac{12}{25} - \frac{1}{25} ln (5)

Dezimale

0.41562 \dots

Schritte zur Lösung

\int_{1}^{5} \frac{ln ( x ^{2} )}{x ^{3}} d x

Wende die partielle Integration an

= [- \frac{ln ( x ^{2} )}{2 x ^{2}} - \int - \frac{1}{x ^{3}} d x]_{1}^{5}

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

= [- \frac{ln ( x ^{2} )}{2 x ^{2}} - \frac{1}{2 x ^{2}}]_{1}^{5}

\frac{ln ( x ^{2} )}{2 x ^{2}} = \frac{ln ( x )}{x ^{2}}

= [- \frac{ln ( x )}{x ^{2}} - \frac{1}{2 x ^{2}}]_{1}^{5}

Berechne die Grenzen:

\frac{12}{25} - \frac{1}{25} ln (5)

= \frac{12}{25} - \frac{1}{25} ln (5)

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