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" 5."int(0)^( pi/2)(1)/(1+cos^(2)x)dx...

" 5."int_(0)^( pi/2)(1)/(1+cos^(2)x)dx

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int_(0)^( pi/4)(1)/(cos^(2)x)dx

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

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

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

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

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

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

int_(0)^(pi//2) (1)/(4+3 cos x)dx

int_(0)^(pi//2) (1)/(4+3 cos x)dx