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If int(cosec^2x)ln(cosx+sqrt(cos2x))dx=f...

If `int(cosec^2x)ln(cosx+sqrt(cos2x))dx`=`f(x)ln(cosx+sqrt(cos2x))+g(x)+f(x)-x+c` then `f^2(x)-g^2(x)` is equal to

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