$\"\"$

\

The improper integral is $\"\"$ .

\

Rewrite the integral as $\"\"$ .

\

The integral is improper because the lower limit is $\"\"$ for which the integral is undefined when plugged into it.

\

$\"\"$ .

\

Consider $\"\"$ .

\

Solve the integral by using integral by parts.

\

Apply integration by parts formula: $\"\"$ .

\

Here $\"\"$ and $\"\"$ .

\

Consider $\"\"$ .

\

Apply derivative on each side with respect to $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

Consider $\"\"$ .

\

Integrate on each side.

\

$\"\"$

\

$\"\"$ .

\

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

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

$\"\"$ .

\

$\"\"$

\

The integral is $\"\"$ .

\

Substitute $\"\"$ in $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ is indetermined.

\

$\"\"$

\

The limit is $\"\"$ .

\

Apply L hospital rule.

\

$\"\"$

\

$\"\"$

\

Apply L hospital rule.

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Therefore, the integral converges to $\"\"$ .

\

$\"\"$

\

Graph:

\

Graph the integrand $\"\"$ .

\

$\"\"$

\

Observe the graph:

\

Using integration capabilities $\"\"$ .

\

$\"\"$

\

The improper integral $\"\"$ is converges to $\"\"$ .