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int(0)^((pi)/(2))(1)/(1+cos2x)dx...

`int_(0)^((pi)/(2))(1)/(1+cos2x)dx`

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int_(0)^((pi)/(2))(1)/(4+5cos x)dx=

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

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

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

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