Check convergence of improper integrals type 2

[bstuan]

Please suggest me how to choose a suitable function (g(x)) so that the convergence property of the following improper integral can be checked by the comparison method:
[math]\int_0^1\frac{x.dx}{tanx-sinx}[/math]

 

[blamocur]

I would start by transforming the expression to use [imath]x[/imath], [imath]\sin x[/imath] and [imath]\cos x[/imath].