$\"\"$

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The integral is $\"\"$ .

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$\"\"$

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Let $\"\"$ .

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Differentiate on each side.

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$\"\"$

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Let $\"\"$ .

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Integrate on each side.

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$\"\"$

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Integration by parts : $\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$

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Case 1 : For $\"\"$ .

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Equation (1) is a undefined.

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If $\"\"$ then $\"\"$ is divergent.

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Case 2 : For $\"\"$ .

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If $\"\"$ then $\"\"$ is convergent.

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$\"\"$

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If $\"\"$ then $\"\"$ is divergent.

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If $\"\"$ then $\"\"$ is convergent.