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Beliebt Rechnen >

integral of xln(\sqrt[3]{x})

Lösung

\int x ln (3 x) d x

Lösung

\frac{1}{3} (\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4}) + C

Schritte zur Lösung

\int x ln (3 x) d x

Vereinfache

ln (3 x) : \frac{1}{3} ln (x)

= \int \frac{1}{3} x ln (x) d x

Entferne die Konstante:

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

= \frac{1}{3} \cdot \int x ln (x) d x

Wende die partielle Integration an

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

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

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

Füge eine Konstante zur Lösung hinzu

= \frac{1}{3} (\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4}) + C

Graph

Beliebte Beispiele

tangent f(x)=-1/x

t an g e n t f (x) = - \frac{1}{x}

derivative f(x)=sqrt(1+x)

d er i v a t i v e f (x) = 1 + x

integral of (pi/6)/0 sin(x)cos^3(x)

\int \frac{\frac{π}{6}}{0} sin (x) cos^{3} (x) d x

inverselaplace 1/(s^2)

in v erse l a pl a ce \frac{1}{s ^{2}}

integral of-(2000)/(x^2)

\int - \frac{2000}{x ^{2}} d x