$\"\"$

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The integral function is $\"\"$ .

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Rewrite the integral.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Trigonometric identities : $\"\"$ .

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$\"\"$

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Double angle trigonometric identity: $\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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

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$\"\"$

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Solve the equation $\"\"$

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Let $\"\"$

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Differentiate on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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Change of the limits

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If $\"\"$

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If $\"\"$

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Substitute $\"\"$ and $\"\"$ in equation of $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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Solve the equation $\"\"$

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$\"\"$

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Double angle trigonometric identity: $\"\"$ .

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$\"\"$

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$\"\"$

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

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$\"\"$

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$\"\"$ .

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$\"\"$

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$\"\"$ .