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Beliebt Rechnen >

integral of ln(5x+1)

Lösung

\int ln (5 x + 1) d x

Lösung

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

Schritte zur Lösung

\int ln (5 x + 1) 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 + 1

ein

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

Vereinfache

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of sqrt((5-4x)/(4-4x))

\int \frac{5 - 4 x}{4 - 4 x} d x

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(\partial)/(\partial y)((9y)/(x^3))

\frac{\partial}{\partial y} (\frac{9 y}{x ^{3}})

integral of 0.5e^{-x}

\int 0.5 e^{- x} d x

integral of 4/((x^2+1)^{3/2)}

\int \frac{4}{( x ^{2} + 1 ) ^{\frac{3}{2}}} d x