$\"\"$

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The integral is $\"\"$ .

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Double angle identity $\"\"$ .

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$\"\"$

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Sum and difference rule of integration : $\"\"$ .

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$\"\"$ .

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$\"\"$

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Consider $\"\"$ .

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Integration by parts formula : $\"\"$ .

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Consider $\"\"$ .

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$\"\"$ .

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Apply derivative on each side.

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$\"\"$ .

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$\"\"$

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Integrate on each side.

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$\"\"$

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Substitute $\"\"$ in the integration by parts fromula.

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$\"\"$

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Substitute $\"\"$ in equation (1).

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$\"\"$

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$\"\"$ .

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$\"\"$

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$\"\"$ .