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Beliebt Rechnen >

integral of 2/3 x^2ln(x)

Lösung

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

Lösung

\frac{2}{3} (\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9}) + C

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die partielle Integration an

= \frac{2}{3} (\frac{1}{3} x^{3} ln (x) - \int \frac{x ^{2}}{3} d x)

\int \frac{x ^{2}}{3} d x = \frac{x ^{3}}{9}

= \frac{2}{3} (\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9})

Füge eine Konstante zur Lösung hinzu

= \frac{2}{3} (\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9}) + C

Graph

Beliebte Beispiele

limit as x approaches 1 of ((x^2-5))/x

x \to 1 lim (\frac{( x ^{2} - 5 )}{x})

limit as x approaches 5 of sqrt(8x+5)

x \to 5 lim (8 x + 5)

derivative of e^{x^2y}-2x-2y

\frac{d}{d x} (e^{x^{2} y} - 2 x - 2 y)

integral of x^3e^{12x}

\int x^{3} e^{12 x} d x

derivative of (x^4+3x^{-1})

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