Integrate:
two more discrepancies here. in the first post you had $\displaystyle \sqrt{1 ~{\color{red}+}~ x^2}$ in the denominator, which made the integral impossible.
secondly, now this $\displaystyle T_i(x)$ appears and you never told us anything about it. Please try to describe the problem completely, we do not have your text book
I was wrong in the first entry. it is -
T0(x) = 1, T1(x)=x
In general, Ti(x)= cos[i arccos x], i > 0
It is posted on this website (its question 3b)
http://www.math.niu.edu/~dattab/math435/HW4.pdf