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Beliebt Rechnen >

integral of x*ln(2x)

Lösung

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

Lösung

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

Schritte zur Lösung

\int x ln (2 x) d x

Wende die partielle Integration an

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

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

derivative of 2x^3-21x^2+60x

\frac{d}{d x} (2 x^{3} - 21 x^{2} + 60 x)

integral of 1/(sqrt(4-25x^2))

\int \frac{1}{4 - 25 x ^{2}} d x

integral from 0 to 1 of x/(x^2+9)

\int_{0}^{1} \frac{x}{x ^{2} + 9} d x

integral of 1/((3x+1)^2)

\int \frac{1}{( 3 x + 1 ) ^{2}} d x

integral from 0 to infinity of t^2

\int_{0}^{\infty} t^{2} d t