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int(sin2x)/(1+sin^(2)x)dx=...

int(sin2x)/(1+sin^(2)x)dx=

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Evaluate int(sin2x)/(1+cos^(2)x)dx .

Evaluate : int_(0)^((pi)/(2))(sin 2x)/(1+sin^(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