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

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

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integral of (1/x)sin(1/x)

integral

(\frac{1}{x}) sin (\frac{1}{x})

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

Solution steps

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

Apply u-substitution

= \int - \frac{sin ( u )}{u} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int \frac{sin ( u )}{u} d u

Use the nonelementary integral:

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

= - Si (u)

Substitute back

u = \frac{1}{x}

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

Add a constant to the solution

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

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