What is the integral of 1-cos(1/x) ?

The integral of 1-cos(1/x) is x(1-cos(1/x))-\Si(1/x)+C

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integral of 1-cos(1/x)

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

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

Solution steps

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

Apply Integration By Parts

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

= 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})

Add a constant to the solution

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

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What is the integral of 1-cos(1/x) ?
The integral of 1-cos(1/x) is x(1-cos(1/x))-\Si(1/x)+C