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

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

Apply u-substitution

: \int sin (v) d v

= \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

\int \frac{1}{( 3 - 2 x )} d x

\int (1 - x) (1 - x^{2}) d x

\int (x - 1)^{2} (x - 2) d x

\int \frac{x ^{3} + 1}{x x} d x

\int x^{2} e^{\frac{x ^{2}}{2}} d x

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