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

The integral of ((sin(ln(x)))/x) is -cos(ln(x))+C

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integral of ((sin(ln(x)))/x)

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

- cos (ln (x)) + C

Solution steps

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

Apply u-substitution

= \int sin (u) d u

Use the common integral:

\int sin (u) d u = - cos (u)

= - cos (u)

Substitute back

u = ln (x)

= - cos (ln (x))

Add a constant to the solution

= - cos (ln (x)) + C

What is the integral of ((sin(ln(x)))/x) ?
The integral of ((sin(ln(x)))/x) is -cos(ln(x))+C