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Beliebt Rechnen >

integral of 4sqrt(x)ln(x)

Lösung

\int 4 x ln (x) d x

Lösung

4 (\frac{2}{3} x^{\frac{3}{2}} ln (x) - \frac{4}{9} x^{\frac{3}{2}}) + C

Schritte zur Lösung

\int 4 x ln (x) d x

Entferne die Konstante:

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

= 4 \cdot \int x ln (x) d x

Wende die partielle Integration an

= 4 (\frac{2}{3} x^{\frac{3}{2}} ln (x) - \int \frac{2}{3} x^{\frac{1}{2}} d x)

\int \frac{2}{3} x^{\frac{1}{2}} d x = \frac{4}{9} x^{\frac{3}{2}}

= 4 (\frac{2}{3} x^{\frac{3}{2}} ln (x) - \frac{4}{9} x^{\frac{3}{2}})

Füge eine Konstante zur Lösung hinzu

= 4 (\frac{2}{3} x^{\frac{3}{2}} ln (x) - \frac{4}{9} x^{\frac{3}{2}}) + C

Graph

Beliebte Beispiele

integral of (2x^3)/((x^4+5))

\int \frac{2 x ^{3}}{( x ^{4} + 5 )} d x

tangent 1.12x^3-6.3x^2-11.2x+1.2

t an g e n t 1.12 x^{3} - 6.3 x^{2} - 11.2 x + 1.2

t an g e n t x^{2} e^{x}

derivative of (i+xj+2xk/(sqrt(5x^2+1)))

\frac{d}{d x} (\frac{i + x j + 2 x k}{5 x ^{2} + 1})

derivative of 3x^{2/3}-3

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