What is the integral of cos(ln(x)) 1/x ?

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

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integral of cos(ln(x)) 1/x

\int cos (ln (x)) \frac{1}{x} d x

sin (ln (x)) + C

Solution steps

\int cos (ln (x)) \frac{1}{x} d x

Simplify

cos (ln (x)) \frac{1}{x} : \frac{cos ( ln ( x ) )}{x}

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

Apply u-substitution

: \int cos (u) d u

= \int cos (u) d u

Use the common integral:

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

= sin (u)

Substitute back

u = ln (x)

= sin (ln (x))

Add a constant to the solution

= sin (ln (x)) + C

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