Given that

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Substitute the value of u = e^2x and du = e^xdx

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Substitute u = sins and du = cos(s)ds then

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Write

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Integrate the sum terms by term and constant

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For integral cos2s substitute p = 2s ===> dp = 2ds

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The integral of cosp is sinp

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The integration of 1 is s

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Substitute back for p = 2s

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Substitute back

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Substitute the value that

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Take common

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The integral of the given equation is

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