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" 52."int(-0)^((pi)/(2))((sin x+cos x)^(...

" 52."int_(-0)^((pi)/(2))((sin x+cos x)^(2))/(sqrt(1+sin^(2)x))dx

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The value of I=int_(0)^((pi)/(2))((sin x+cos x)^(2))/(sqrt(1+sin2x))dx

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

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

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

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

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

The value of int _(0)^(pi//2) ((sin x + cos x)^(2))/(sqrt(1+sin 2x) dx is

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

int_(0)^(pi/2)(sin^(2)x*cos x)dx=