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.

Multiply by .

Multiply by .

Reorder and .

Integrate by parts using the formula , where and .

Solving for , we find that = .

Replace all occurrences of with .

Exponentiation and log are inverse functions.

Exponentiation and log are inverse functions.

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