>>526
{(e^x-e^(sinx))/x^3} = e^(sinx){(e^(x-sinx)-1)/x^3}

e^(x-sinx) = e^{(1/6)x^3+o(x^3)} = 1+(1/6)x^3+o(x^3)

lim(x→0)　{(e^x-e^(sinx))/x^3} = 1/6


∫0→1　{(x^2+1)/(x^4+1)}dx
=(1/2)∫0→1　{1/(x^2+√2x+1)+1/(x^2-√2x+1)}dx
=(1/2)∫0→1　[1/{(x+1/√2)^2+1/2} + 1/{(x-1/√2)^2+1/2}] dx
=(1/2)*√2*{arctan(√2+1)+arctan(√2-1)}
=(√2/4)π