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Beliebt Rechnen >

integral of-2xln(x)

Lösung

\int - 2 x ln (x) d x

Lösung

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

Schritte zur Lösung

\int - 2 x ln (x) d x

Entferne die Konstante:

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

= - 2 \cdot \int x ln (x) d x

Wende die partielle Integration an

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

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

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

Vereinfache

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of-2x^3

\int - 2 x^{3} d x

(\partial}{\partial x}(\frac{x^2)/2+(y^3)/3)

\frac{\partial}{\partial x} (\frac{x ^{2}}{2} + \frac{y ^{3}}{3})

derivative f(x)=5ex

d er i v a t i v e f (x) = 5 e x

d/(dt)(t^{1/2})

\frac{d}{d t} (t^{\frac{1}{2}})

limit as x approaches 0 of ((3+x^2)-9)/x

x \to 0 lim (\frac{( 3 + x ^{2} ) - 9}{x})