$\"\"$

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The improper integral is $\"\"$ .

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Apply partial fraction decomposition.

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$\"\"$ .

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$\"\"$

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Equate coefficients on both sides.

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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Now consider $\"\"$ .

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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.