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Beliebt Rechnen >

integral of (ln(5x)+5)/x

Lösung

\int \frac{ln ( 5 x ) + 5}{x} d x

Lösung

\frac{ln ^{2} ( 5 x )}{2} + 5 ln ∣ x ∣ + C

Schritte zur Lösung

\int \frac{ln ( 5 x ) + 5}{x} d x

Multipliziere aus

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

= \int \frac{ln ( 5 x )}{x} + \frac{5}{x} d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{ln ( 5 x )}{x} d x + \int \frac{5}{x} d x

\int \frac{ln ( 5 x )}{x} d x = \frac{ln ^{2} ( 5 x )}{2}

\int \frac{5}{x} d x = 5 ln ∣ x ∣

= \frac{ln ^{2} ( 5 x )}{2} + 5 ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= \frac{ln ^{2} ( 5 x )}{2} + 5 ln ∣ x ∣ + C

Graph

Beliebte Beispiele

integral from 7 to 9 of 1/(x^2-1)

\int_{7}^{9} \frac{1}{x ^{2} - 1} d x

derivative of x^3+x^2+6/x

\frac{d}{d x} (x^{3} + x^{2} + \frac{6}{x})

derivative of (x^2-1/x)

\frac{d}{d x} (\frac{x ^{2} - 1}{x})

derivative of x^2sin((2pi/x))

\frac{d}{d x} (x^{2} sin (\frac{2 π}{x}))

integral of x^-

\int x^{-} d x