The integral is .

Definition of an improper integral :

If  exists for every number , then  provoded this limit exists (as a finite number).

.

Consider .

Let , then .

Boundaries : from  to .

Substitute corresponding values in .

Substitute ,  and boundaries in above equation.

.

Substitute  in equation (1).

Since (finite value), the integral is convergent.

The integral is convergent and the value is .