Prove Convergence of Integral (1/x)sin(1/x)dx from 0 to 1

[covariance64]

Homework Statement

Show that the integral of (1/x)sin(1/x)dx from 0 to 1 is converges absolutely?

Homework Equations

The Attempt at a Solution

Should we use the comparison test in this situation?

 

[quasar987]

Try a change of variables first.

 

[elabed haidar]

Homework Statement

Show that the integral of (1/x)sin(1/x)dx from 0 to 1 is converges absolutely?

Homework Equations

The Attempt at a Solution

Should we use the comparison test in this situation?

change of variable u=1/x you will get from 1 to infinite integral of -sinu over u after that you do integration by parts and you will get your answer sinu / u is always convergent