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Beliebt Rechnen >

integral of 3sqrt(x)ln(x)

Lösung

\int 3 x ln (x) d x

Lösung

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

Schritte zur Lösung

\int 3 x ln (x) d x

Entferne die Konstante:

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

= 3 \cdot \int x ln (x) d x

Wende die partielle Integration an

= 3 (\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}}

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

Vereinfache

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

derivative of sqrt(cos(4x))

\frac{d}{d x} (cos (4 x))

integral of 2/(3x+5)

\int \frac{2}{3 x + 5} d x

integral from 0 to 4 of x(0.5-0.125x)

\int_{0}^{4} x (0.5 - 0.125 x) d x

y^{^{''}} = 2

(\partial)/(\partial x)(K(x)^{1/3}L^{2/3})

\frac{\partial}{\partial x} (K (x)^{\frac{1}{3}} L^{\frac{2}{3}})