Final answer:
To find the integral of arctan(x)/x as a power series, substitute the power series expansion of arctan(x) into the integral, integrate each term, and sum them up to get the power series representation of the integral.
Step-by-step explanation:
To find the integral of arctan(x)/x as a power series, we can start by using the power series expansion of arctan(x) = x - x^3/3 + x^5/5 - x^7/7 + ...
Then, we can substitute this expansion into the integral, integrate each term of the power series, and sum them up.
The resulting power series representation of the integral of arctan(x)/x is:
∫ arctan(x)/x dx = x - x^3/9 + x^5/45 - x^7/315 + ...