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

The integral of 1/x sin(ln(x)) is -cos(ln(x))+C

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

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

- cos (ln (x)) + C

Solution steps

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

Apply u-substitution

: \int sin (u) d u

= \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

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