$\"\"$

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The gamma function is $\"\"$ , $\"\"$ .

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Find the values of $\"\"$ and $\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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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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(b)

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Use integration by parts show that $\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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Formula for integration by parts : $\"\"$ .

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

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Consider $\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$ .

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Consider $\"\"$ .

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Integrate on each side.

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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$\"\"$

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Since $\"\"$ .

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$\"\"$

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Therefore, $\"\"$ .

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$\"\"$

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(c)

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The integral is $\"\"$ .

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Since $\"\"$ .

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$\"\"$

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$\"\"$

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Therefore, $\"\"$ .

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$\"\"$

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(a) $\"\"$ , $\"\"$ and $\"\"$ .

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(b) $\"\"$ .

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(c) $\"\"$ .