1. The problem statement, all variables and given/known data arctan x = ∫du/(1+u2), from 0 to x 2. Relevant equations 3. The attempt at a solution I noticed that 1/(1+u2) = 1/(1+u2)1/2 × 1/(1+u2)1/2. I decided to take the taylor series expansion of 1/(1+u2)1/2, square the result and then integrate. I got 1/(1+u2)1/2 = 1 - u2 + 3u4/8 - 15u6/48... When squaring that result, I get 1/1+u2 = 1 - u2 +5u4/8 ... When I integrate, the first 2 terms are fine but the x5/8 should be x5/5. Did I make a mistake, or is my method of "cheating" the interval of convergence for the binomial series somehow falsifying the result?