$\"\"$

\

The integral is $\"\"$ .

\

If $\"\"$ is continuous on the interval $\"\"$ and has an infinite discontinuity at $\"\"$ , then $\"\"$ , the limit exists then function is convergent.

\

$\"\"$ is discontinuous at $\"\"$ .

\

$\"\"$ .

\

The integral is continuous at $\"\"$ , then the function is convergent. $\"\"$

\

$\"\"$

\

$\"\"$

\

Apply formula $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

Therefore, the series is converges at $\"\"$ .

\

$\"\"$

\

Graph:

\

Graph the integrand $\"\"$ .

\

$\"\"$

\

Observe the graph:

\

Using integration capabilities $\"\"$ .

\

$\"\"$

\

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