$\"\"$

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The integral is $\"\"$ .

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

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

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$\"\"$ .

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

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$\"\"$

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$\"\"$

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Apply formula $\"\"$ .

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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 diverges.

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$\"\"$

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The improper integral $\"\"$ is diverges.