f(x)=∫(0,x)sint/t dtf'(x)=sinx/x=1-x^2/3!+x^4/5!+..+(-1)^(n-1)x^(2n-2)/(2n-1)!+.由于f(0)=0,积分得：f(x)=x-x^3/3!3+x^5/5!5+..+(-1)^(n-1)x^(2n-1)/(2n-1)!(2n-1)+.
积分范围(0,x)∫sint/t dt,把这个式子展开成迈克劳林级数
f(x)=∫(0,x)sint/t dtf'(x)=sinx/x=1-x^2/3!+x^4/5!+..+(-1)^(n-1)x^(2n-2)/(2n-1)!+.由于f(0)=0,积分得：f(x)=x-x^3/3!3+x^5/5!5+..+(-1)^(n-1)x^(2n-1)/(2n-1)!(2n-1)+.