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Beliebt Rechnen >

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

Lösung

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

Lösung

- \frac{ln ^{2} ( x )}{x} + 2 (- \frac{ln ( x )}{x} - \frac{1}{x}) + C

Schritte zur Lösung

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

Vereinfache

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

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

Wende die partielle Integration an

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

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

= - \frac{ln ^{2} ( x )}{x} - (- 2 (- \frac{ln ( x )}{x} - \frac{1}{x}))

Vereinfache

= - \frac{ln ^{2} ( x )}{x} + 2 (- \frac{ln ( x )}{x} - \frac{1}{x})

Füge eine Konstante zur Lösung hinzu

= - \frac{ln ^{2} ( x )}{x} + 2 (- \frac{ln ( x )}{x} - \frac{1}{x}) + C

Graph

Beliebte Beispiele

limit as x approaches pi of 6

x \to π lim (6)

(d^2Q)/(dt^2)-7(dQ)/(dt)+5Q=0

\frac{d ^{2} Q}{d t ^{2}} - 7 \frac{d Q}{d t} + 5 Q = 0

integral of (cos(t))/(sqrt(1+sin^2(t)))

\int \frac{cos ( t )}{1 + sin ^{2} ( t )} d t

derivative of 7/((x+1^2))

\frac{d}{d x} (\frac{7}{( x + 1 ) ^{2}})

derivative of 1/(1+1/4 x)

\frac{d}{d x} (\frac{1}{1 + \frac{1}{4} x})