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Beliebt Rechnen >

integral of ((ln(x))/(sqrt(x^3)))

Lösung

\int (\frac{ln ( x )}{x ^{3}}) d x

Lösung

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

Schritte zur Lösung

\int \frac{ln ( x )}{x ^{3}} d x

x^{3} = x^{\frac{3}{2}},

angenommen

x \geq 0

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

Wende die partielle Integration an

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

\int - \frac{2}{x x} d x = \frac{4}{x}

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

derivative of (10/((x-2)^3))

\frac{d}{d x} (\frac{10}{( x - 2 ) ^{3}})

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integral of (2x-2)e^{-x}

\int (2 x - 2) e^{- x} d x

derivative of 5x^7e^x

\frac{d}{d x} (5 x^{7} e^{x})