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Beliebt Rechnen >

integral of (x-5)ln(x)

Lösung

\int (x - 5) ln (x) d x

Lösung

ln (x) (\frac{x ^{2}}{2} - 5 x) - \frac{1}{2} (\frac{x ^{2}}{2} - 10 x) + C

Schritte zur Lösung

\int (x - 5) ln (x) d x

Wende die partielle Integration an

= ln (x) (\frac{x ^{2}}{2} - 5 x) - \int \frac{1}{2} (x - 10) d x

\int \frac{1}{2} (x - 10) d x = \frac{1}{2} (\frac{x ^{2}}{2} - 10 x)

= ln (x) (\frac{x ^{2}}{2} - 5 x) - \frac{1}{2} (\frac{x ^{2}}{2} - 10 x)

Füge eine Konstante zur Lösung hinzu

= ln (x) (\frac{x ^{2}}{2} - 5 x) - \frac{1}{2} (\frac{x ^{2}}{2} - 10 x) + C

Graph

Beliebte Beispiele

steigung y=3-4x^2,(-1,-1)

s l o p e y = 3 - 4 x^{2}, (- 1, - 1)

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\int 8 sin (x) cos (x) d x

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x \to 2 lim (\frac{1}{2 - x})

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\int sinh (3 - 4 x) d x