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Beliebt Rechnen >

integral from 1 to 1.5 of x^2ln(x)

Lösung

\int_{1}^{1.5} x^{2} ln (x) d x

Lösung

0.19225 \dots

Schritte zur Lösung

\int_{1}^{1.5} x^{2} ln (x) d x

Wende die partielle Integration an

= [\frac{1}{3} (x^{3} ln (x) - 3 \cdot \int \frac{x ^{2}}{3} d x)]_{1}^{1.5}

\int \frac{x ^{2}}{3} d x = \frac{x ^{3}}{9}

= [\frac{1}{3} (x^{3} ln (x) - 3 \cdot \frac{x ^{3}}{9})]_{1}^{1.5}

Vereinfache

[\frac{1}{3} (x^{3} ln (x) - 3 \cdot \frac{x ^{3}}{9})]_{1}^{1.5} : [0.33333 \dots (x^{3} ln (x) - 0.33333 \dots x^{3})]_{1}^{1.5}

= [0.33333 \dots (x^{3} ln (x) - 0.33333 \dots x^{3})]_{1}^{1.5}

Berechne die Grenzen:

0.19225 \dots

= 0.19225 \dots

Graph

Beliebte Beispiele

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a re a \frac{x}{2}, 3 x^{2} - 1, 0, 0.5

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\int \frac{1}{cos ( θ )} d θ