integral of (ln(1/x))^2

Lösung

\int (ln (\frac{1}{x}))^{2} d x

x ln^{2} (x) - 2 (x ln (x) - x) + C

Schritte zur Lösung

\int (ln (\frac{1}{x}))^{2} d x

Vereinfache

(ln (\frac{1}{x}))^{2} : ln^{2} (x)

= \int ln^{2} (x) d x

Wende die partielle Integration an

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

\int 2 ln (x) d x = 2 (x ln (x) - x)

= x ln^{2} (x) - 2 (x ln (x) - x)

Füge eine Konstante zur Lösung hinzu

= x ln^{2} (x) - 2 (x ln (x) - x) + C

\int \frac{( x - 1 )}{x ^{2} - 4 x + 3} d x

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