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Beliebt Rechnen >

integral of ln(5x+8)

Lösung

\int ln (5 x + 8) d x

Lösung

x ln (5 x + 8) + \frac{8}{5} ln (5 x + 8) - x - \frac{8}{5} + C

Schritte zur Lösung

\int ln (5 x + 8) d x

Wende U-Substitution an

= \int ln (u) \frac{1}{5} d u

Entferne die Konstante:

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

= \frac{1}{5} \cdot \int ln (u) d u

Wende die partielle Integration an

= \frac{1}{5} (u ln (u) - \int 1 d u)

\int 1 d u = u

= \frac{1}{5} (u ln (u) - u)

Setze in

u = 5 x + 8

ein

= \frac{1}{5} ((5 x + 8) ln (5 x + 8) - (5 x + 8))

Vereinfache

\frac{1}{5} ((5 x + 8) ln (5 x + 8) - (5 x + 8)) : x ln (5 x + 8) + \frac{8}{5} ln (5 x + 8) - x - \frac{8}{5}

= x ln (5 x + 8) + \frac{8}{5} ln (5 x + 8) - x - \frac{8}{5}

Füge eine Konstante zur Lösung hinzu

= x ln (5 x + 8) + \frac{8}{5} ln (5 x + 8) - x - \frac{8}{5} + C

Graph

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