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" (a) firse anfry for: "int(0)^( pi/2)(d...

" (a) firse anfry for: "int_(0)^( pi/2)(dx)/(1+sqrt(tan x))=(pi)/(4)

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

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

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

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

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

int_(pi//6)^(pi//3) (dx)/(1 + sqrt(tan x)) =

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

int_(0)^((pi)/(4))sqrt(tan x)dx