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Beliebt Rechnen >

integral of arctan(2/x)

Lösung

\int arctan (\frac{2}{x}) d x

Lösung

x arctan (\frac{2}{x}) + ln 4 + x^{2} + C

Schritte zur Lösung

\int arctan (\frac{2}{x}) d x

Wende die partielle Integration an

= x arctan (\frac{2}{x}) - \int - \frac{2 x}{4 + x ^{2}} d x

\int - \frac{2 x}{4 + x ^{2}} d x = - ln 4 + x^{2}

= x arctan (\frac{2}{x}) - (- ln 4 + x^{2})

Vereinfache

= x arctan (\frac{2}{x}) + ln 4 + x^{2}

Füge eine Konstante zur Lösung hinzu

= x arctan (\frac{2}{x}) + ln 4 + x^{2} + C

Graph

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