Convergence of Improper Integral: Can a Comparison Test Be Used?

[aostraff]

Homework Statement

I'm trying to show that this improper integral converges
\int_{0}^{1} \sin \left ( x + \frac{1}{x} \right )dx

Homework Equations

The Attempt at a Solution

I thought a comparison test would be nice but I can't think of the right one if that is the way to go. I don't think a substitution of u = x + 1/x works too well as well.

Thanks.

 

[Mark44]

-1 <= sin(x + 1/x) <= 1

 

[aostraff]

I see. Thanks.