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

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

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

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

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

Solution steps

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

Apply u-substitution

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

= \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

(5 t^{3}) \cdot (e^{t})

\frac{1}{1 + 9 x ^{2}}

\int \frac{z ^{4} + 10 z ^{3}}{2 z ^{2}} d z

(- 2, - 4), (2, - 4)

\frac{d}{d x} (x \cdot y)

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