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int(0)^( pi/2)(1)/(4cos^(2)x+9sin^(2)x)d...

int_(0)^( pi/2)(1)/(4cos^(2)x+9sin^(2)x)dx=

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If I_(1)=int_(0)^(pi//2)(cos^(2)x)/(1+cos^(2)x)dx,I_(2)=int_(0)^(pi//2)(sin^(2)x)/(1+sin^(2)x)dx , I_(3)=int_(0)^(pi//2)(1+2cos^(2)x.sin^(2)x)/(4+2cos^(2)xsin^(2)x)dx , then