integral from 1 to 2 of (3x+2)ln(x)

Lösung

\int_{1}^{2} (3 x + 2) ln (x) d x

10 ln (2) - \frac{17}{4}

Dezimale

2.68147 \dots

Schritte zur Lösung

\int_{1}^{2} (3 x + 2) ln (x) d x

Wende die partielle Integration an

= [ln (x) (\frac{3 x ^{2}}{2} + 2 x) - \int \frac{1}{2} (3 x + 4) d x]_{1}^{2}

\int \frac{1}{2} (3 x + 4) d x = \frac{1}{2} (\frac{3 x ^{2}}{2} + 4 x)

= [ln (x) (\frac{3 x ^{2}}{2} + 2 x) - \frac{1}{2} (\frac{3 x ^{2}}{2} + 4 x)]_{1}^{2}

Berechne die Grenzen:

10 ln (2) - \frac{17}{4}

= 10 ln (2) - \frac{17}{4}

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