$\"\"$

The integral is $\"\"$ .

Definition of an improper integral :

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

$\"\"$

Consider $\"\"$ .

Let $\"\"$ .

Differentiate on each side with respect to $\"\"$ .

$\"\"$

Boundaries : from $\"\"$ to $\"\"$ .

Substitute corresponding values in equation $\"\"$ .

$\"\"$

Power rule of integral : $\"\"$ .

$\"\"$

$\"\"$ .

Since $\"\"$ (finite value), the integral is convergent. $\"\"$

The integral is convergent and the value is $\"\"$ .