$\"\"$

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The improper integral is $\"\"$ .

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

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$\"\"$ .

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Consider $\"\"$ .

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

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

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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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$\"\"$ .

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Consider $\"\"$ .

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Apply integration on each side.

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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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The integral is $\"\"$ .

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

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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 integral converges to $\"\"$ .

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$\"\"$

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Graph:

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Graph the integrand $\"\"$ .

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$\"\"$

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Observe the graph:

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Using integration capabilities $\"\"$ .

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$\"\"$

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