int (1/p+(1/(2p^2(1+pi)))z^2 + ((6+(2-\pi)p)/(24p^3(1+pi)^2))z^4+((90+30(2-\pi)p+(16-13\pi+\pi^2)p^2)/(720p^4(1+pi)^3))z^6)/y dy, where z=cos(2y), p=ln(1+1/pi)