Problem:
Find the third order expansion of the following function around 3:
$\cos ^{-1}\left(\frac{x^5}{2}\right)$
Answer:
$-\frac{365 (x-1)^3}{9 \sqrt{3}}-\frac{85 (x-1)^2}{6 \sqrt{3}}-\frac{5 (x-1)}{\sqrt{3}}+\frac{\pi }{3}$
{'source': 'AMPS', 'file': 'amps/mathematica/calculus/series_expansion/31347.txt'}