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Beliebt Rechnen >

integral of 3(ln(x))^2

Lösung

\int 3 (ln (x))^{2} d x

Lösung

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

Schritte zur Lösung

\int 3 (ln (x))^{2} d x

Entferne die Konstante:

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

= 3 \cdot \int (ln (x))^{2} d x

Wende die partielle Integration an

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

\int 2 ln (x) d x = 2 (x ln (x) - x)

= 3 (x ln^{2} (x) - 2 (x ln (x) - x))

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of x(x-3)

\int x (x - 3) d x

derivative of (cos(x^3)^2)

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

2xy+x^3=(xdy)/(dx)

2 x y + x^{3} = \frac{x d y}{d x}

integral of (sin(3t+10))/(cos^2(3t+10))

\int \frac{sin ( 3 t + 10 )}{cos ^{2} ( 3 t + 10 )} d t

derivative of 2sqrt(x)ln(x)

\frac{d}{d x} (2 x ln (x))