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

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

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integral of (cos(ln(y)))/y

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

sin (ln (y)) + C

Solution steps

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

Apply u-substitution

: \int cos (u) d u

= \int cos (u) d u

Use the common integral:

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

= sin (u)

Substitute back

u = ln (y)

= sin (ln (y))

Add a constant to the solution

= sin (ln (y)) + C

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