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Beliebt Rechnen >

integral of (2x-1)ln(x)

Lösung

\int (2 x - 1) ln (x) d x

Lösung

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

Schritte zur Lösung

\int (2 x - 1) ln (x) d x

Wende die partielle Integration an

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

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

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

Vereinfache

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of (2x^2+x+15)/(x+3)

\int \frac{2 x ^{2} + x + 15}{x + 3} d x

integral from 1 to 2 of 2-x

\int_{1}^{2} 2 - x d x

y^{^{'}} = x y + 3

limit as x approaches-infinity of 2+e^x

x \to - \infty lim (2 + e^{x})

derivative of 0.1x

\frac{d}{d x} (0.1 x)