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Beliebt Rechnen >

integral of-tln(t)

Lösung

\int - t ln (t) d t

Lösung

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

Schritte zur Lösung

\int - t ln (t) d t

Entferne die Konstante:

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

= - \int t ln (t) d t

Wende die partielle Integration an

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

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

tangent x^2,\at x=0

t an g e n t x^{2}, at x = 0

(\partial)/(\partial y)(x^3yz^2)

\frac{\partial}{\partial y} (x^{3} y z^{2})

integral of [ 4/(16x^2+1)]

\int [\frac{4}{16 x ^{2} + 1}] d x

tangent f(x)=x^2-5x+5,(6,11)

t an g e n t f (x) = x^{2} - 5 x + 5, (6, 11)

(\partial)/(\partial s)(s+t)

\frac{\partial}{\partial s} (s + t)