Find the Maclaurin Series of integral from 0 to x of et2 I k

Solution

e^(-t^2) = 1 - (t^2) + (t^4)/2! - (t^6)/3! + (t^8)/4! -............

Integral from 0 to x of e^(-t^2) dt,

= (x) - (x^3)/3 + (x^5)/5.2! - (x^7)/7.3! + (x^9)/9.4! - (x^11)/11.5! +.......