$\"\"$

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The improper integral is $\"\"$ .

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Apply the limit to the integral.

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$\"\"$ .

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Consider $\"\"$ .

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Apply derivative on each side.

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$\"\"$ .

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Substitute $\"\"$ and $\"\"$ in the integral.

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$\"\"$ .

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$\"\"$ .

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Substiute $\"\"$ .

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$\"\"$

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Therefore, the limit does not exist.

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$\"\"$

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The improper integral $\"\"$ diverges.