f(x) = integral from 0 to x

((cos(t)-1)/(t^2))

I took the known taylor series of cos(t)

= Sigma n=0 to infinity

((-1)^n t^2n))

2n! t^2

and moved the t^2 to the t exponential

((-1)^n t^2n-2))

2n!

What would the next step be?

If I take the integral...

((-1)^n x^2n-1))

2n!(2n-1)

from n=1 to infinity

Is this correct?

Thanks.