>>229
　exp(y) ≧ 1+y より
I1 = ∫[0→1] exp(-x^6) dx < ∫[0→1] 1/(1+x^6) dx

部分分数に分解すると
1/(1+x^6)
　= (1/3)(2-xx)/(1-xx+x^4) + (1/3)/(1+xx)
　= (1/2)(1-xx)/(1-xx+x^4) + (1/6)(1+xx)/(1-xx+x^4) + (1/3)/(1+xx)
　= (1/2)(1-xx)/(1-xx+x^4) + (1/12)/[xx -(√3)x +1] + (1/12)/[xx+（√3)x +1] + (1/3)/(1+xx),

I1 = [ (1/(4√3))log{[xx+(√3)x+1]/[xx-(√3)x+1]} + (1/6)arctan(2x-√3) + (1/6)arctan(2x+√3) + (1/3)arctan(x)](x=0→1)
　= (1/6){π +(√3)log(2+√3)}
　= 0.90377177375

　exp(y) ≧ e･y より
I2 =∫[1,a] exp(-x^6) dx < ∫[1,a] 1/(e･x^6)dx
　= [ -1/(5e･x^5) ](x=1→a)
　< 1/(5e)
　= 0.0735758882343

∴∫[1,a] exp(-x^6) dx < 0.97734766198306