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)

\int cos (\frac{1}{x}) d 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{d y}{d t} - \frac{3}{t} y = 2 t^{3} e^{2 t}, y (1) = 0

\int 24 x d x

\frac{d y}{d t} = - k y

9 x - 4 y (x^{2} + 1) (\frac{d y}{d x}) = 0

\int \frac{x}{( x + 4 ) ^{\frac{1}{3}}} d x

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