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Beliebt Rechnen >

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

Lösung

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

Lösung

x - ln x^{2} + 1 + C

Schritte zur Lösung

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

\int 1 d x = x

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

= x - ln x^{2} + 1

Füge eine Konstante zur Lösung hinzu

= x - ln x^{2} + 1 + C

Graph

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