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

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

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integral of cos(1/x)

integral

cos (\frac{1}{x})

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

Solution steps

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

Apply Integration By Parts

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

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

Simplify

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

Add a constant to the solution

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

\frac{x + 1}{x}

sin^{4} (x) cos^{2} (x)

y = - sin^{3} (x)

\frac{( x ^{4} )}{( x ^{3} - 1 )}

\frac{x}{( x ^{2} + 4 )}

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