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For x in(0, (pi)/(2)) If int(tan x sqrt(...

For `x in(0, (pi)/(2))` If `int(tan x sqrt(sec x)(1+cos^(2)x))/(sqrt(cos x+sin^(2)x))dx=2sqrt(f(x)+1)+c` and `f((pi)/(3))=(3)/(2)` then `[f((pi)/(4))] =`( where `[.]` denotes G.I.F )

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