What is the integral of sin(x^{-1}) ?

The integral of sin(x^{-1}) is xsin(1/x)-\Ci(1/x)+C

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integral of sin(x^{-1})

\int sin (x^{- 1}) d x

x sin (\frac{1}{x}) - Ci (\frac{1}{x}) + C

Solution steps

\int sin (x^{- 1}) d x

x^{- 1} = \frac{1}{x}

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

Apply Integration By Parts

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

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

= x sin (\frac{1}{x}) - Ci (\frac{1}{x})

Add a constant to the solution

= x sin (\frac{1}{x}) - Ci (\frac{1}{x}) + C

What is the integral of sin(x^{-1}) ?
The integral of sin(x^{-1}) is xsin(1/x)-\Ci(1/x)+C