What is the integral of (cos(ln(2x)))/x ?

The integral of (cos(ln(2x)))/x is sin(ln(2x))+C

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integral of (cos(ln(2x)))/x

\int \frac{cos ( ln ( 2 x ) )}{x} d x

sin (ln (2 x)) + C

Solution steps

\int \frac{cos ( ln ( 2 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 (2 x))

Add a constant to the solution

= sin (ln (2 x)) + C

\int \frac{x ^{2} + 16 x - 4}{x ^{3} - 4 x} d x

y = \frac{1}{3 + 2 x}, (2, \frac{1}{7})

7 x - 6 y x^{2} + 1 \frac{d y}{d x} = 0

\frac{d y}{d x} = (e^{4 x + 3 y})

(sin (π) x)^{^{'}}

What is the integral of (cos(ln(2x)))/x ?
The integral of (cos(ln(2x)))/x is sin(ln(2x))+C