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int(0)^(pi//2)(dx)/((1+sqrt(tanx)))=(pi)...

`int_(0)^(pi//2)(dx)/((1+sqrt(tanx)))=(pi)/(4)`

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int_(0)^(pi//2)(1)/(1+sqrt(tan x))dx=

int_(0)^((pi)/(2))(dx)/(1+sqrt(tan x))=int_(0)^((pi)/(2))(dx)/(1+sqrt(cot x))=(pi)/(4)

int_(0)^(pi//2)(1)/((1+sqrt(cotx)))dx=?

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int_(0)^(pi//2)(tanx)/((1+tanx))dx=?

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int_(0)^(pi//2)(dx)/(1+e^(sqrt(2)cos(x+(pi)/(4)))) is equal to

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int_(0)^(a)(dx)/(x+sqrt(a^(2)-x^(2)))=(pi)/(4)