integral of (x+1)ln(2x+4)

Lösung

\int (x + 1) ln (2 x + 4) d x

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

Schritte zur Lösung

\int (x + 1) ln (2 x + 4) d x

Wende die partielle Integration an

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

\int \frac{x}{2} d x = \frac{x ^{2}}{4}

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

Füge eine Konstante zur Lösung hinzu

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