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Beliebt Rechnen >

integral of 5xln(5x)

Lösung

\int 5 x ln (5 x) d x

Lösung

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

Schritte zur Lösung

\int 5 x ln (5 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 (5 x) d x

Wende die partielle Integration an

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

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of 1/(2x^2)

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

fläche y=(7t-4),(0,0.5)

a re a y = (7 t - 4), (0, 0.5)

derivative of x^{tan(x})

\frac{d}{d x} (x^{t a n (x)})

integral from 1 to 9 of 2/(sqrt(x))

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

derivative of 2/3 x^2(x^3-1)

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