What is the integral of (sin(ln(3x)))/x ?

The integral of (sin(ln(3x)))/x is -cos(ln(3x))+C

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integral of (sin(ln(3x)))/x

\int \frac{sin ( ln ( 3 x ) )}{x} d x

- cos (ln (3 x)) + C

Solution steps

\int \frac{sin ( ln ( 3 x ) )}{x} d x

Apply u-substitution

= \int \frac{sin ( ln ( u ) )}{u} d u

Apply u-substitution

= \int sin (v) d v

Use the common integral:

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

= - cos (v)

Substitute back

= - cos (ln (3 x))

Add a constant to the solution

= - cos (ln (3 x)) + C

What is the integral of (sin(ln(3x)))/x ?
The integral of (sin(ln(3x)))/x is -cos(ln(3x))+C