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Beliebt Rechnen >

integral of t(ln(t))^2

Lösung

\int t (ln (t))^{2} d t

Lösung

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

Schritte zur Lösung

\int t (ln (t))^{2} d t

Wende die partielle Integration an

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

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

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

Vereinfache

= \frac{1}{2} t^{2} ln^{2} (t) - \frac{1}{2} t^{2} ln (t) + \frac{t ^{2}}{4}

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

derivative arcsin(1/t)

d er i v a t i v e arcsin (\frac{1}{t})

derivative of sin(4x-5)

\frac{d}{d x} (sin (4 x - 5))

tangent f(x)=(x^2+36)(2x+21),\at x=-4

t an g e n t f (x) = (x^{2} + 36) (2 x + 21), at x = - 4

derivative f(x)=-4x^2

d er i v a t i v e f (x) = - 4 x^{2}

limit as x approaches 0 of (sin(4x)cos(3x))/(7x)

x \to 0 lim (\frac{sin ( 4 x ) cos ( 3 x )}{7 x})