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int(0)^( pi/4)(dx)/(1+cos2x)...

int_(0)^( pi/4)(dx)/(1+cos2x)

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Show that int_(0)^(pi//4)(dx)/(cos^(4)x - cos^(2)x sin^(2) x + sin^(4)x) = (pi)/(2)

Show that int_(0)^(pi/4)(dx)/(cos^(4)x - cos^(2)x sin^(2) x + sin^(4) x) = pi/2