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Beliebt Rechnen >

integral of-ln(x)x

Lösung

\int - ln (x) x d x

Lösung

- \frac{1}{2} x^{2} ln (x) + \frac{x ^{2}}{4} + C

Schritte zur Lösung

\int - ln (x) x d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int ln (x) x d x

Wende die partielle Integration an

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

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

= - (\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4})

Vereinfache

= - \frac{1}{2} x^{2} ln (x) + \frac{x ^{2}}{4}

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{2} x^{2} ln (x) + \frac{x ^{2}}{4} + C

Graph

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