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Beliebt Rechnen >

integral of xln(x+2)

Lösung

\int x ln (x + 2) d x

Lösung

ln (x + 2) (\frac{1}{2} (x + 2)^{2} - 2 (x + 2)) - \frac{1}{4} (x^{2} - 4 x - 12) + C

Schritte zur Lösung

\int x ln (x + 2) d x

Wende U-Substitution an

= \int (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

\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)

Setze in

u = x + 2

ein

= ln (x + 2) (\frac{( x + 2 ) ^{2}}{2} - 2 (x + 2)) - \frac{1}{2} (\frac{( x + 2 ) ^{2}}{2} - 4 (x + 2))

Vereinfache

ln (x + 2) (\frac{( x + 2 ) ^{2}}{2} - 2 (x + 2)) - \frac{1}{2} (\frac{( x + 2 ) ^{2}}{2} - 4 (x + 2)) : ln (x + 2) (\frac{1}{2} (x + 2)^{2} - 2 (x + 2)) - \frac{1}{4} (x^{2} - 4 x - 12)

= ln (x + 2) (\frac{1}{2} (x + 2)^{2} - 2 (x + 2)) - \frac{1}{4} (x^{2} - 4 x - 12)

Füge eine Konstante zur Lösung hinzu

= ln (x + 2) (\frac{1}{2} (x + 2)^{2} - 2 (x + 2)) - \frac{1}{4} (x^{2} - 4 x - 12) + C

Graph

Beliebte Beispiele

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