integral of 1-cos(1/x)

Lösung

\int 1 - cos (\frac{1}{x}) d x

x (1 - cos (\frac{1}{x})) - Si (\frac{1}{x}) + C

Schritte zur Lösung

\int 1 - cos (\frac{1}{x}) d x

Wende die partielle Integration an

= x (1 - cos (\frac{1}{x})) - \int - \frac{sin ( \frac{1}{x} )}{x} d x

\int - \frac{sin ( \frac{1}{x} )}{x} d x = Si (\frac{1}{x})

= x (1 - cos (\frac{1}{x})) - Si (\frac{1}{x})

Füge eine Konstante zur Lösung hinzu

= x (1 - cos (\frac{1}{x})) - Si (\frac{1}{x}) + C

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