What is the integral of (cos(ln(4x)))/x ?

The integral of (cos(ln(4x)))/x is sin(ln(4x))+C

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integral of (cos(ln(4x)))/x

\int \frac{cos ( ln ( 4 x ) )}{x} d x

sin (ln (4 x)) + C

Solution steps

\int \frac{cos ( ln ( 4 x ) )}{x} d x

Apply u-substitution

: \int \frac{cos ( ln ( u ) )}{u} d u

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

Apply u-substitution

: \int cos (v) d v

= \int cos (v) d v

Use the common integral:

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

= sin (v)

Substitute back

= sin (ln (4 x))

Add a constant to the solution

= sin (ln (4 x)) + C

\int (2 x + 8) d x

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

\int e^{x} sin (π x) d x

\int x^{2} + a d x

What is the integral of (cos(ln(4x)))/x ?
The integral of (cos(ln(4x)))/x is sin(ln(4x))+C