integral of (arctan(1/x))

Lösung

\int (arctan (\frac{1}{x})) d x

x arctan (\frac{1}{x}) + \frac{1}{2} ln 1 + x^{2} + C

Schritte zur Lösung

\int arctan (\frac{1}{x}) d x

Wende die partielle Integration an

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

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

= x arctan (\frac{1}{x}) - (- \frac{1}{2} ln 1 + x^{2})

Vereinfache

= x arctan (\frac{1}{x}) + \frac{1}{2} ln 1 + x^{2}

Füge eine Konstante zur Lösung hinzu

= x arctan (\frac{1}{x}) + \frac{1}{2} ln 1 + x^{2} + C

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