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Beliebt Rechnen >

integral of ((2+ln(x^2)))/x

Lösung

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

Lösung

2 ln ∣ x ∣ + ln^{2} (x) + C

Schritte zur Lösung

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

Multipliziere aus

\frac{2 + ln ( x ^{2} )}{x} : \frac{2}{x} + \frac{ln ( x ^{2} )}{x}

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

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

= 2 ln ∣ x ∣ + ln^{2} (x)

Füge eine Konstante zur Lösung hinzu

= 2 ln ∣ x ∣ + ln^{2} (x) + C

Graph

Beliebte Beispiele

integral of (20)/(x^3+x^2)

\int \frac{20}{x ^{3} + x ^{2}} d x

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\int x (x^{2} - 3)^{5} d x

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\int \frac{x ^{2} + 3 x + 3}{x ^{2} - 3 x + 2} d x

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\int (2 x + 5) x + 3 d x

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\int sec^{3} (8 x) tan (8 x) d x