# Evaluate integral of cos( natural log of x) with respect to x

Let . Then , so . Rewrite using and .
Reorder and .
Integrate by parts using the formula , where and .
Since is constant with respect to , move out of the integral.
Simplify the expression.
Multiply by .
Multiply by .
Reorder and .
Integrate by parts using the formula , where and .
Solving for , we find that = .
Replace all occurrences of with .