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Beliebt Rechnen >

integral of (ln^2(x))/(sqrt(x^5))

Lösung

\int \frac{ln ^{2} ( x )}{x ^{5}} d x

Lösung

- \frac{2 ln ^{2} ( x )}{3 x ^{\frac{3}{2}}} + \frac{4}{3} (- \frac{2 ln ( x )}{3 x ^{\frac{3}{2}}} - \frac{4}{9 x ^{\frac{3}{2}}}) + C

Schritte zur Lösung

\int \frac{ln ^{2} ( x )}{x ^{5}} d x

Wende die partielle Integration an

= - \frac{2 ln ^{2} ( x )}{3 x ^{\frac{3}{2}}} - \int - \frac{4 ln ( x )}{3 x ^{\frac{5}{2}}} d x

\int - \frac{4 ln ( x )}{3 x ^{\frac{5}{2}}} d x = - \frac{4}{3} (- \frac{2 ln ( x )}{3 x ^{\frac{3}{2}}} - \frac{4}{9 x ^{\frac{3}{2}}})

= - \frac{2 ln ^{2} ( x )}{3 x ^{\frac{3}{2}}} - (- \frac{4}{3} (- \frac{2 ln ( x )}{3 x ^{\frac{3}{2}}} - \frac{4}{9 x ^{\frac{3}{2}}}))

Vereinfache

= - \frac{2 ln ^{2} ( x )}{3 x ^{\frac{3}{2}}} + \frac{4}{3} (- \frac{2 ln ( x )}{3 x ^{\frac{3}{2}}} - \frac{4}{9 x ^{\frac{3}{2}}})

Füge eine Konstante zur Lösung hinzu

= - \frac{2 ln ^{2} ( x )}{3 x ^{\frac{3}{2}}} + \frac{4}{3} (- \frac{2 ln ( x )}{3 x ^{\frac{3}{2}}} - \frac{4}{9 x ^{\frac{3}{2}}}) + C

Graph

Beliebte Beispiele

integral of (x^5-x^3)

\int (x^{5} - x^{3}) d x

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