The integral is .

Rewrite the integral as .

Consider the second integral on right side .

Now apply comparison value theorem for above integral.

Consider the fact  and it implies that  .

Comparison theorem:

Suppose that  and  are continuous functions with  for ,

1. If  is convergent, then  is convergent.

2.If  is divergent, then  is also divergent.

Here  and 

Since  is a finite value, it is convergent.

By comparison theorem,  is convergent.

 is convergent, it follows that  is also convergent.

 and  are convergent, then is convergent.

 is convergent.