integral from 2 to 5 of xln(x+2)

Lösung

\int_{2}^{5} x ln (x + 2) d x

- \frac{9}{4} + \frac{21}{2} ln (7)

Dezimale

18.18205 \dots

Schritte zur Lösung

\int_{2}^{5} x ln (x + 2) d x

Wende U-Substitution an

= \int_{4}^{7} (u - 2) ln (u) d u

Wende die partielle Integration an

= [ln (u) (\frac{u ^{2}}{2} - 2 u) - \int \frac{1}{2} (u - 4) d u]_{4}^{7}

\int \frac{1}{2} (u - 4) d u = \frac{1}{2} (\frac{u ^{2}}{2} - 4 u)

= [ln (u) (\frac{u ^{2}}{2} - 2 u) - \frac{1}{2} (\frac{u ^{2}}{2} - 4 u)]_{4}^{7}

Berechne die Grenzen:

- \frac{9}{4} + \frac{21}{2} ln (7)

= - \frac{9}{4} + \frac{21}{2} ln (7)

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