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[" 12."int(0)^( pi/2)(sin x+cos x)/(sin ...

[" 12."int_(0)^( pi/2)(sin x+cos x)/(sin x+cos x)dx=int_(0)^(1)(sqrt(sin x+cos x))/(1+sqrt(cot x))=(pi)/(4)],[" 13."int_(0)^( pi/2)(dx)/(1+sqrt(tan x))=int_(0)^( pi/2)(dx)/(1+sqrt(cot x))=(pi)/(4)],[qquad pi/4]

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

int_(0)^(pi)(cos x)/(1+sqrt(sin x))dx=

int_(0)^(pi//2) (Cos x)/(1+Sin x) dx=

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int _(0) ^(pi//2) (sin x +cos x)/ sqrt(1+sin 2x )" "dx=

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Prove that int_(0)^(pi//2) (sin x -cos x)/(1+sin x cos x)dx = 0 .

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int_(0)^( pi)((sin x+cos x)^(2))/(sqrt(1+sin2x))dx