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Beliebt Rechnen >

integral of x^{1/2}ln(x)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die partielle Integration an

= \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}}

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

derivative of a+bx^2

\frac{d}{d x} (a + b x^{2})

limit as x approaches-2 of g(x)

x \to - 2 lim (g (x))

fläche y=e^{-0.6x},y=1.4x+1,x=0,x=5

a re a y = e^{- 0.6 x}, y = 1.4 x + 1, x = 0, x = 5

derivative of in(x-1)

\frac{d}{d x} (in (x - 1))

y^{''}-y=e^{-x}

y^{^{''}} - y = e^{- x}