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Beliebt Rechnen >

integral of ln(4x+1)

Lösung

\int ln (4 x + 1) d x

Lösung

x ln (4 x + 1) + \frac{1}{4} ln (4 x + 1) - x - \frac{1}{4} + C

Schritte zur Lösung

\int ln (4 x + 1) d x

Wende U-Substitution an

= \int ln (u) \frac{1}{4} d u

Entferne die Konstante:

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

= \frac{1}{4} \cdot \int ln (u) d u

Wende die partielle Integration an

= \frac{1}{4} (u ln (u) - \int 1 d u)

\int 1 d u = u

= \frac{1}{4} (u ln (u) - u)

Setze in

u = 4 x + 1

ein

= \frac{1}{4} ((4 x + 1) ln (4 x + 1) - (4 x + 1))

Vereinfache

\frac{1}{4} ((4 x + 1) ln (4 x + 1) - (4 x + 1)) : x ln (4 x + 1) + \frac{1}{4} ln (4 x + 1) - x - \frac{1}{4}

= x ln (4 x + 1) + \frac{1}{4} ln (4 x + 1) - x - \frac{1}{4}

Füge eine Konstante zur Lösung hinzu

= x ln (4 x + 1) + \frac{1}{4} ln (4 x + 1) - x - \frac{1}{4} + C

Graph

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