$\"\"$

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The integral is $\"\"$ .

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

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If $\"\"$ is continuous on the interval $\"\"$ , except for some $\"\"$ in $\"\"$ at which $\"\"$ has an infinite

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discontinuity, then $\"\"$ .

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The improper integral on the left diverges if either of the improper integrals on the right diverges.

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$\"\"$ .

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$\"\"$

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$\"\"$

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Consider $\"\"$ .

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

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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Apply formula : $\"\"$ .

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$\"\"$

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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

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$\"\"$

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Grpah :

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Graph the integrand as $\"\"$ .

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$\"\"$

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$\"\"$

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