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Beliebt Rechnen >

integral of ln(9x+7)

Lösung

\int ln (9 x + 7) d x

Lösung

x ln (9 x + 7) + \frac{7}{9} ln (9 x + 7) - x - \frac{7}{9} + C

Schritte zur Lösung

\int ln (9 x + 7) d x

Wende U-Substitution an

= \int ln (u) \frac{1}{9} d u

Entferne die Konstante:

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

= \frac{1}{9} \cdot \int ln (u) d u

Wende die partielle Integration an

= \frac{1}{9} (u ln (u) - \int 1 d u)

\int 1 d u = u

= \frac{1}{9} (u ln (u) - u)

Setze in

u = 9 x + 7

ein

= \frac{1}{9} ((9 x + 7) ln (9 x + 7) - (9 x + 7))

Vereinfache

\frac{1}{9} ((9 x + 7) ln (9 x + 7) - (9 x + 7)) : x ln (9 x + 7) + \frac{7}{9} ln (9 x + 7) - x - \frac{7}{9}

= x ln (9 x + 7) + \frac{7}{9} ln (9 x + 7) - x - \frac{7}{9}

Füge eine Konstante zur Lösung hinzu

= x ln (9 x + 7) + \frac{7}{9} ln (9 x + 7) - x - \frac{7}{9} + C

Graph

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