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Beliebt Rechnen >

integral of 1/2 x^2ln(x)-(x^2)/4-(x^2)/2

Lösung

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

Lösung

\frac{1}{2} (\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9}) - \frac{x ^{3}}{12} - \frac{x ^{3}}{6} + C

Schritte zur Lösung

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

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

\int \frac{x ^{2}}{4} d x = \frac{x ^{3}}{12}

\int \frac{x ^{2}}{2} d x = \frac{x ^{3}}{6}

= \frac{1}{2} (\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9}) - \frac{x ^{3}}{12} - \frac{x ^{3}}{6}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} (\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9}) - \frac{x ^{3}}{12} - \frac{x ^{3}}{6} + C

Graph

Beliebte Beispiele

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