$\"\"$

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The integral is $\"\"$ .

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Definition of an improper integral :

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If $\"\"$ exists for every number $\"\"$ , then $\"\"$ provoded this limit exists (as a finite number).

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$\"\"$

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Let $\"\"$ .

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Partial fraction decomposition.

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$\"\"$

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$\"\"$

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$\"\"$

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Solve the above equations find values of $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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

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Substitute the $\"\"$ and $\"\"$ values in equation $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Formula of integral : $\"\"$ .

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$\"\"$

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Therefore, $\"\"$ .

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Since $\"\"$ (infinite value), the integral is divergent. $\"\"$

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The integral is divergent and the value is $\"\"$ .