integral of ln(t^2)

Lösung

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

2 t ln (t) - 2 t + C

Schritte zur Lösung

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

Wende die partielle Integration an

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

\int 2 d t = 2 t

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

Wende log Regel an

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

angenommen

x \geq 0

= 2 t ln (t) - 2 t

Füge eine Konstante zur Lösung hinzu

= 2 t ln (t) - 2 t + C

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