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Beliebt Rechnen >

integral of (2x+6)ln(x)

Lösung

\int (2 x + 6) ln (x) d x

Lösung

x^{2} ln (x) + 6 x ln (x) - \frac{x ^{2}}{2} - 6 x + C

Schritte zur Lösung

\int (2 x + 6) ln (x) d x

Wende die partielle Integration an

= ln (x) (x^{2} + 6 x) - \int x + 6 d x

\int x + 6 d x = \frac{x ^{2}}{2} + 6 x

= ln (x) (x^{2} + 6 x) - (\frac{x ^{2}}{2} + 6 x)

Vereinfache

ln (x) (x^{2} + 6 x) - (\frac{x ^{2}}{2} + 6 x) : x^{2} ln (x) + 6 x ln (x) - \frac{x ^{2}}{2} - 6 x

= x^{2} ln (x) + 6 x ln (x) - \frac{x ^{2}}{2} - 6 x

Füge eine Konstante zur Lösung hinzu

= x^{2} ln (x) + 6 x ln (x) - \frac{x ^{2}}{2} - 6 x + C

Graph

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