$\"\"$

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The laplace transform of $\"\"$ is $\"\"$ .

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Find the laplace transform when $\"\"$ .

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

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$\"\"$

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$\"\"$

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Apply formula 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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$\"\"$

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$\"\"$ .

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Consider $\"\"$ .

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Apply integral on each side.

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$\"\"$

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$\"\"$ .

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Substitute corresponding values 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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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Therefore, $\"\"$ , $\"\"$ .

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$\"\"$

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The laplace transform of $\"\"$ is $\"\"$ , $\"\"$ .