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

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

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integral of sin(1/x)

integral

sin (\frac{1}{x})

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

Solution steps

\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

= 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

a^{2} - x^{2}

x^{2} a^{2} - x^{2}

\frac{1}{( 1 + x ^{2} ) ^{\frac{1}{2}}}

\frac{sin ( x )}{2}

\frac{1}{( x ^{4} + 1 )}

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