>>123
1-x^2+√(1+x^2)=0 を解くと x=±√3 だから
∫_[-√3,√3] √(1-x^2+√(1+x^2)) dx=
http://www.wolframalpha.com/input/?i=integrate+%281-x%5E2%2B%281%2Bx%5E2%29%5E%281%2F2%29%29%5E%281%2F2%29+from+x%3D-3%5E%281%2F2%29+to+3%5E%281%2F2%29