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Beliebt Rechnen >

integral of 5xln(2x)

Lösung

\int 5 x ln (2 x) d x

Lösung

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

Schritte zur Lösung

\int 5 x ln (2 x) d x

Entferne die Konstante:

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

= 5 \cdot \int x ln (2 x) d x

Wende die partielle Integration an

= 5 (\frac{1}{2} x^{2} ln (2 x) - \int \frac{x}{2} d x)

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

= 5 (\frac{1}{2} x^{2} ln (2 x) - \frac{x ^{2}}{4})

Füge eine Konstante zur Lösung hinzu

= 5 (\frac{1}{2} x^{2} ln (2 x) - \frac{x ^{2}}{4}) + C

Graph

Beliebte Beispiele

derivative of 2^{x/2}

\frac{d}{d x} (2^{\frac{x}{2}})

tangent-1/x ,\at x=3

t an g e n t - \frac{1}{x}, at x = 3

derivative of 1/(2sqrt(x+4))

\frac{d}{d x} (\frac{1}{2 x + 4})

derivative ln(sqrt((4x+1)/(x^2-1)))

d er i v a t i v e ln (\frac{4 x + 1}{x ^{2} - 1})

integral from 0 to 5 of w/(w-2)

\int_{0}^{5} \frac{w}{w - 2} d w