arctan x*√(1+cosx)是奇函数，故原式=∫[-3π/4,3π/4]√(1+cosx)dx=√2∫[-3π/4,3π/4](cos(x/2)dx=2√2sin(x/2)|[-3π/4,3π/4]=4√2sin(3π/8)=2√(4+2√2)
