Step 1:

The integral is .

Rewrite the integral as

Consider the first integral on right side .

From the interval above integral has a finite value, it is convergent.

is convergent.

Consider the second integral on right side .

Now we can apply comparison value theorem for above integral.

Consider the fact and it implies that  .

Comparison theorem:

Suppose that are continuous functions with ,

1. If is convergent, then is convergent.

2.If is divergent, then is also divergent.

Here and

Hence is a finite value, it is convergent.

By comparison theorem, is convergent.

is convergent.

Since the two integrals on right side part of Equation (1) is convergent, So the left side part is also convergent.

is convergent.

Solution:

is convergent.