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Beliebt Rechnen >

integral of 2tln(t)

Lösung

\int 2 t ln (t) d t

Lösung

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

Schritte zur Lösung

\int 2 t ln (t) d t

Entferne die Konstante:

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

= 2 \cdot \int t ln (t) d t

Wende die partielle Integration an

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

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

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

Vereinfache

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

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