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Beliebt Rechnen >

integral of ln(3x+2)

Lösung

\int ln (3 x + 2) d x

Lösung

x ln (3 x + 2) + \frac{2}{3} ln (3 x + 2) - x - \frac{2}{3} + C

Schritte zur Lösung

\int ln (3 x + 2) d x

Wende U-Substitution an

= \int ln (u) \frac{1}{3} d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int ln (u) d u

Wende die partielle Integration an

= \frac{1}{3} (u ln (u) - \int 1 d u)

\int 1 d u = u

= \frac{1}{3} (u ln (u) - u)

Setze in

u = 3 x + 2

ein

= \frac{1}{3} ((3 x + 2) ln (3 x + 2) - (3 x + 2))

Vereinfache

\frac{1}{3} ((3 x + 2) ln (3 x + 2) - (3 x + 2)) : x ln (3 x + 2) + \frac{2}{3} ln (3 x + 2) - x - \frac{2}{3}

= x ln (3 x + 2) + \frac{2}{3} ln (3 x + 2) - x - \frac{2}{3}

Füge eine Konstante zur Lösung hinzu

= x ln (3 x + 2) + \frac{2}{3} ln (3 x + 2) - x - \frac{2}{3} + C

Graph

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