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

Lösung

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

4 ln (2) - \frac{3}{2}

Dezimale

1.27258 \dots

Schritte zur Lösung

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

Wende die partielle Integration an

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

\int x d x = \frac{x ^{2}}{2}

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

\frac{1}{2} x^{2} ln (x^{2}) = x^{2} ln (x)

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

Berechne die Grenzen:

4 ln (2) - \frac{3}{2}

= 4 ln (2) - \frac{3}{2}

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