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Beliebt Rechnen >

integral of x^2ln(x^4)

Lösung

\int x^{2} ln (x^{4}) d x

Lösung

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

Schritte zur Lösung

\int x^{2} ln (x^{4}) d x

Wende die partielle Integration an

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

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

= \frac{1}{3} x^{3} ln (x^{4}) - \frac{4 x ^{3}}{9}

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

derivative of (sin(x)^4)

\frac{d}{d x} ((sin (x))^{4})

derivative of cos(10x)

\frac{d}{d x} (cos (10 x))

xy^'+y^'-(x+1)cos(x)+y=0

x y^{^{'}} + y^{^{'}} - (x + 1) cos (x) + y = 0

(dx)/(dt)=5x(9-x)

\frac{d x}{d t} = 5 x (9 - x)

integral of cos^2(1/3)x

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