函数f(x)=∫(1-cos√x)/x dx (上限x,下限0)的麦克劳林级数为

cosx=1-x^2/2!+x^4/4!-.+(-1)^nx^(2n)/(2n)!+.
cos√x=1-x/2!+x^2/4!-.+(-1)^nx^(n)/(2n)!+.
1-cos√x=x/2!-x^2/4!+.+(-1)^(n-1)x^(n)/(2n)!+.
(1-cos√x)/x=1/2!-x/4!+.+(-1)^(n-1)x^(n-1)/(2n)!+.
所以：f(x)=∫(1-cos√x)/x dx
=∫(1/2!-x/4!+.+(-1)^(n-1)x^(n-1)/(2n)!+.）dx
=x/2!-x^2/4!2+.+(-1)^(n-1)x^(n)/(2n)!n+.
=∑(1,+∞)(-1)^(n-1)x^(n)/[(2n)!n]