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Beliebt Rechnen >

integral of 1/x+2/(x^2)+10^x

Lösung

\int \frac{1}{x} + \frac{2}{x ^{2}} + 1 0^{x} d x

Lösung

ln ∣ x ∣ - \frac{2}{x} + \frac{1 0 ^{x}}{ln ( 10 )} + C

Schritte zur Lösung

\int \frac{1}{x} + \frac{2}{x ^{2}} + 1 0^{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{1}{x} d x + \int \frac{2}{x ^{2}} d x + \int 1 0^{x} d x

\int \frac{1}{x} d x = ln ∣ x ∣

\int \frac{2}{x ^{2}} d x = - \frac{2}{x}

\int 1 0^{x} d x = \frac{1 0 ^{x}}{ln ( 10 )}

= ln ∣ x ∣ - \frac{2}{x} + \frac{1 0 ^{x}}{ln ( 10 )}

Füge eine Konstante zur Lösung hinzu

= ln ∣ x ∣ - \frac{2}{x} + \frac{1 0 ^{x}}{ln ( 10 )} + C

Graph

Beliebte Beispiele

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\int x^{2} cos (4) x^{3} d x

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\int e^{- b x^{2}} d x

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\int t^{2} cos (3 t) d t

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\int \frac{1}{x ^{2} ln ( x )} d x

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\int \frac{1}{x ^{2} + x + 2} d x