$\"\"$

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The integral is $\"\"$ .

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$\"\"$ .

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Apply integration by parts : $\"\"$ .

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Let $\"\"$ .

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Let $\"\"$ , then $\"\"$ .

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Substitute these values in the integration by parts formula.

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$\"\"$

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$\"\"$

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Consider $\"\"$ .

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Partial fraction decomposition.

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$\"\"$

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Compare coefficients of $\"\"$ terms on each side.

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$\"\"$

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Compare coefficients of $\"\"$ terms on each side.

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$\"\"$

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Compare constant terms on each side.

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$\"\"$

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If $\"\"$ , then $\"\"$ .

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$\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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$\"\"$ .