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$\int_{0}^{\frac{\pi}{4}}( \sec 2x -\tan 2x )\ dx$
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$\int$sec2x = 1/2 * ln|sec2x + tan2x|

$\int$tan2x = -1/2 * ln|cos2x|

$\int_{0}^{\prod/4}$(sec2x - tan2x) = $\int_{0}^{\prod/4}$(1/2ln|sec2x + tan2x|+1/2ln|cos2x|) = $\int_{0}^{\prod/4}$(1/2ln|1+sin2x|) = 1/2ln2
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