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

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

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integral of (sin(ln(y)))/y

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

- cos (ln (y)) + C

Solution steps

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

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 (y)

= - cos (ln (y))

Add a constant to the solution

= - cos (ln (y)) + C

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