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int(0)^(pi//4)(dx)/((1+cos2x))...

`int_(0)^(pi//4)(dx)/((1+cos2x))`

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`int_(0)^(pi//4)(dx)/(1+cos2x)=int_(0)^(pi//4)(1)/(2)sec^(2)xdx=(1)/(2)[tanx]_(0)^(pi//4)=(1)/(2)(1-0)=(1)/(2)`.
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