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\displaystyle \cos(x) = 1-\frac{x^2}{2!}+\frac{x^4}{4!}-\frac{x^6}{6!}+\frac{x^8}{8!}+ \cdots \\[br]\displaystyle \cos(x^2) = 1-\frac{x^4}{2!}+\frac{x^8}{4!}-\frac{x^{12}}{6!}+\frac{x^{16}}{8!}+\cdots\\[br]\displaystyle \int \cos(x^2) \ dx = x-\frac{x^5}{2! \times 5}+\frac{x^9}{4! \times 9}-\frac{x^{13}}{6! \times 13}+\frac{x^{17}}{8! \times 17} + O(x^{21}) + C[br]
\displaystyle \cos(x) = 1-\frac{x^2}{2!}+\frac{x^4}{4!}-\frac{x^6}{6!}+\frac{x^8}{8!}+ \cdots \\[br]\displaystyle \cos(x^2) = 1-\frac{x^4}{2!}+\frac{x^8}{4!}-\frac{x^{12}}{6!}+\frac{x^{16}}{8!}+\cdots\\[br]\displaystyle \int \cos(x^2) \ dx = x-\frac{x^5}{2! \times 5}+\frac{x^9}{4! \times 9}-\frac{x^{13}}{6! \times 13}+\frac{x^{17}}{8! \times 17} + O(x^{21}) + C[br]
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