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" 3."int(0)^( pi/2)(cos x)/((1+sin^(2)x)...

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

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3. int_(0)^( pi/2)( sin2 x)/(1+cos^(2)x)dx

If A = int_(0)^((pi)/(2))(sin^(3)x)/(1+cos^(2)s)dx and B=int_(0)^((pi)/(2))(cos^(2)x)/(1+sin^(2)x)dx , then (2A)/(B) is equal to

If A = int_(0)^((pi)/(2))(sin^(3)x)/(1+cos^(2)s)dx and B=int_(0)^((pi)/(2))(cos^(2)x)/(1+sin^(2)x)dx , then (2A)/(B) is equal to

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

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

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

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