The integral expression  converges.

Consider .

Let .

Differentiate on each side.

Substitute corresponding values in the integral.

If , then 

Substitute above values in .

Therefore, .

Consider .

Apply L-Hospital rule to find the limit, since the expression tends to indeterminate form .

Property of limits : .

.

Substitute above result in equation .

If , then above expression tends to .

If , then expression tends to .

If , then above expression tends to a finite number .

If , Integral tends to a finite number .