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

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

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

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

3 sin (ln (x)) + C

Solution steps

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

Take the constant out:

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

= 3 \cdot \int \frac{cos ( ln ( x ) )}{x} d x

Apply u-substitution

= 3 \cdot \int cos (u) d u

Use the common integral:

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

= 3 sin (u)

Substitute back

u = ln (x)

= 3 sin (ln (x))

Add a constant to the solution

= 3 sin (ln (x)) + C

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