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Beliebt Rechnen >

integral of (ln(x^2))/(x^4)

Lösung

\int \frac{ln ( x ^{2} )}{x ^{4}} d x

Lösung

- \frac{2 ln ( x )}{3 x ^{3}} - \frac{2}{9 x ^{3}} + C

Schritte zur Lösung

\int \frac{ln ( x ^{2} )}{x ^{4}} d x

Wende die partielle Integration an

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

\int - \frac{2}{3 x ^{4}} d x = \frac{2}{9 x ^{3}}

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

Wende log Regel an

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

angenommen

x \geq 0

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

Füge eine Konstante zur Lösung hinzu

= - \frac{2 ln ( x )}{3 x ^{3}} - \frac{2}{9 x ^{3}} + C

Graph

Beliebte Beispiele

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\int cos (x) e^{x} d x