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Beliebt Rechnen >

integral of 5xln(x^3)

Lösung

\int 5 x ln (x^{3}) d x

Lösung

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

Schritte zur Lösung

\int 5 x ln (x^{3}) d x

Entferne die Konstante:

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

= 5 \cdot \int x ln (x^{3}) d x

Wende die partielle Integration an

= 5 (\frac{1}{2} x^{2} ln (x^{3}) - \int \frac{3 x}{2} d x)

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

= 5 (\frac{1}{2} x^{2} ln (x^{3}) - \frac{3 x ^{2}}{4})

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

= 5 (\frac{3}{2} x^{2} ln (x) - \frac{3 x ^{2}}{4})

Füge eine Konstante zur Lösung hinzu

= 5 (\frac{3}{2} x^{2} ln (x) - \frac{3 x ^{2}}{4}) + C

Graph

Beliebte Beispiele

fläche e^x,e^{-2x},x=ln(5)

a re a e^{x}, e^{- 2 x}, x = ln (5)

integral of 28x^3-15x^2+8x

\int 28 x^{3} - 15 x^{2} + 8 x d x

derivative (x-7)/(-5x-10)

d er i v a t i v e \frac{x - 7}{- 5 x - 10}

derivative of x^nln(x)

\frac{d}{d x} (x^{n} ln (x))

inverselaplace 9/((s+3)^2)

in v erse l a pl a ce \frac{9}{( s + 3 ) ^{2}}