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

The integral of (cos(4ln(x)))/x is 1/4 sin(4ln(x))+C

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

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

\frac{1}{4} sin (4 ln (x)) + C

Solution steps

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

Apply u-substitution

: \int \frac{cos ( u )}{4} d u

= \int \frac{cos ( u )}{4} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{4} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{4} sin (u)

Substitute back

u = 4 ln (x)

= \frac{1}{4} sin (4 ln (x))

Add a constant to the solution

= \frac{1}{4} sin (4 ln (x)) + C

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What is the integral of (cos(4ln(x)))/x ?
The integral of (cos(4ln(x)))/x is 1/4 sin(4ln(x))+C