integral from 1 to 2 of ln(x^2)

Lösung

\int_{1}^{2} ln (x^{2}) d x

4 ln (2) - 2

Dezimale

0.77258 \dots

Schritte zur Lösung

\int_{1}^{2} ln (x^{2}) d x

Wende die partielle Integration an

= [x ln (x^{2}) - \int 2 d x]_{1}^{2}

\int 2 d x = 2 x

= [x ln (x^{2}) - 2 x]_{1}^{2}

Wende log Regel an

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

angenommen

x \geq 0

= [2 x ln (x) - 2 x]_{1}^{2}

Berechne die Grenzen:

4 ln (2) - 2

= 4 ln (2) - 2

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