本次共计算 1 个题目：每一题对 x 求 4 阶导数。
    注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{ln(\frac{(2x + 1)}{(2x - 1)})}{12} - \frac{1}{(12x - 2)} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{1}{12}ln(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)}) - \frac{1}{(12x - 2)}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{1}{12}ln(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)}) - \frac{1}{(12x - 2)}\right)}{dx}\\=&\frac{\frac{1}{12}(2(\frac{-(2 + 0)}{(2x - 1)^{2}})x + \frac{2}{(2x - 1)} + (\frac{-(2 + 0)}{(2x - 1)^{2}}))}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})} - (\frac{-(12 + 0)}{(12x - 2)^{2}})\\=&\frac{-x}{3(2x - 1)^{2}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})} - \frac{1}{6(2x - 1)^{2}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})} + \frac{1}{6(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})(2x - 1)} + \frac{12}{(12x - 2)^{2}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-x}{3(2x - 1)^{2}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})} - \frac{1}{6(2x - 1)^{2}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})} + \frac{1}{6(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})(2x - 1)} + \frac{12}{(12x - 2)^{2}}\right)}{dx}\\=&\frac{-(\frac{-2(2 + 0)}{(2x - 1)^{3}})x}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})} - \frac{(\frac{-(2(\frac{-(2 + 0)}{(2x - 1)^{2}})x + \frac{2}{(2x - 1)} + (\frac{-(2 + 0)}{(2x - 1)^{2}}))}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}})x}{3(2x - 1)^{2}} - \frac{1}{3(2x - 1)^{2}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})} - \frac{(\frac{-2(2 + 0)}{(2x - 1)^{3}})}{6(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})} - \frac{(\frac{-(2(\frac{-(2 + 0)}{(2x - 1)^{2}})x + \frac{2}{(2x - 1)} + (\frac{-(2 + 0)}{(2x - 1)^{2}}))}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}})}{6(2x - 1)^{2}} + \frac{(\frac{-(2(\frac{-(2 + 0)}{(2x - 1)^{2}})x + \frac{2}{(2x - 1)} + (\frac{-(2 + 0)}{(2x - 1)^{2}}))}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}})}{6(2x - 1)} + \frac{(\frac{-(2 + 0)}{(2x - 1)^{2}})}{6(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})} + 12(\frac{-2(12 + 0)}{(12x - 2)^{3}})\\=&\frac{4x}{3(2x - 1)^{3}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})} - \frac{4x^{2}}{3(2x - 1)^{4}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} + \frac{2x}{3(2x - 1)^{3}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} - \frac{4x}{3(2x - 1)^{4}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} + \frac{2x}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}(2x - 1)^{3}} - \frac{2}{3(2x - 1)^{2}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})} - \frac{1}{3(2x - 1)^{4}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} + \frac{2}{3(2x - 1)^{3}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})} + \frac{1}{3(2x - 1)^{3}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} + \frac{1}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}(2x - 1)^{3}} - \frac{1}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}(2x - 1)^{2}} - \frac{288}{(12x - 2)^{3}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{4x}{3(2x - 1)^{3}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})} - \frac{4x^{2}}{3(2x - 1)^{4}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} + \frac{2x}{3(2x - 1)^{3}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} - \frac{4x}{3(2x - 1)^{4}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} + \frac{2x}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}(2x - 1)^{3}} - \frac{2}{3(2x - 1)^{2}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})} - \frac{1}{3(2x - 1)^{4}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} + \frac{2}{3(2x - 1)^{3}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})} + \frac{1}{3(2x - 1)^{3}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} + \frac{1}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}(2x - 1)^{3}} - \frac{1}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}(2x - 1)^{2}} - \frac{288}{(12x - 2)^{3}}\right)}{dx}\\=&\frac{4(\frac{-3(2 + 0)}{(2x - 1)^{4}})x}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})} + \frac{4(\frac{-(2(\frac{-(2 + 0)}{(2x - 1)^{2}})x + \frac{2}{(2x - 1)} + (\frac{-(2 + 0)}{(2x - 1)^{2}}))}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}})x}{3(2x - 1)^{3}} + \frac{4}{3(2x - 1)^{3}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})} - \frac{4(\frac{-4(2 + 0)}{(2x - 1)^{5}})x^{2}}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} - \frac{4(\frac{-2(2(\frac{-(2 + 0)}{(2x - 1)^{2}})x + \frac{2}{(2x - 1)} + (\frac{-(2 + 0)}{(2x - 1)^{2}}))}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}})x^{2}}{3(2x - 1)^{4}} - \frac{4*2x}{3(2x - 1)^{4}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} + \frac{2(\frac{-3(2 + 0)}{(2x - 1)^{4}})x}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} + \frac{2(\frac{-2(2(\frac{-(2 + 0)}{(2x - 1)^{2}})x + \frac{2}{(2x - 1)} + (\frac{-(2 + 0)}{(2x - 1)^{2}}))}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}})x}{3(2x - 1)^{3}} + \frac{2}{3(2x - 1)^{3}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} - \frac{4(\frac{-4(2 + 0)}{(2x - 1)^{5}})x}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} - \frac{4(\frac{-2(2(\frac{-(2 + 0)}{(2x - 1)^{2}})x + \frac{2}{(2x - 1)} + (\frac{-(2 + 0)}{(2x - 1)^{2}}))}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}})x}{3(2x - 1)^{4}} - \frac{4}{3(2x - 1)^{4}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} + \frac{2(\frac{-2(2(\frac{-(2 + 0)}{(2x - 1)^{2}})x + \frac{2}{(2x - 1)} + (\frac{-(2 + 0)}{(2x - 1)^{2}}))}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}})x}{3(2x - 1)^{3}} + \frac{2(\frac{-3(2 + 0)}{(2x - 1)^{4}})x}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} + \frac{2}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}(2x - 1)^{3}} - \frac{2(\frac{-2(2 + 0)}{(2x - 1)^{3}})}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})} - \frac{2(\frac{-(2(\frac{-(2 + 0)}{(2x - 1)^{2}})x + \frac{2}{(2x - 1)} + (\frac{-(2 + 0)}{(2x - 1)^{2}}))}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}})}{3(2x - 1)^{2}} - \frac{(\frac{-4(2 + 0)}{(2x - 1)^{5}})}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} - \frac{(\frac{-2(2(\frac{-(2 + 0)}{(2x - 1)^{2}})x + \frac{2}{(2x - 1)} + (\frac{-(2 + 0)}{(2x - 1)^{2}}))}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}})}{3(2x - 1)^{4}} + \frac{2(\frac{-3(2 + 0)}{(2x - 1)^{4}})}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})} + \frac{2(\frac{-(2(\frac{-(2 + 0)}{(2x - 1)^{2}})x + \frac{2}{(2x - 1)} + (\frac{-(2 + 0)}{(2x - 1)^{2}}))}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}})}{3(2x - 1)^{3}} + \frac{(\frac{-3(2 + 0)}{(2x - 1)^{4}})}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} + \frac{(\frac{-2(2(\frac{-(2 + 0)}{(2x - 1)^{2}})x + \frac{2}{(2x - 1)} + (\frac{-(2 + 0)}{(2x - 1)^{2}}))}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}})}{3(2x - 1)^{3}} + \frac{(\frac{-2(2(\frac{-(2 + 0)}{(2x - 1)^{2}})x + \frac{2}{(2x - 1)} + (\frac{-(2 + 0)}{(2x - 1)^{2}}))}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}})}{3(2x - 1)^{3}} + \frac{(\frac{-3(2 + 0)}{(2x - 1)^{4}})}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} - \frac{(\frac{-2(2(\frac{-(2 + 0)}{(2x - 1)^{2}})x + \frac{2}{(2x - 1)} + (\frac{-(2 + 0)}{(2x - 1)^{2}}))}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}})}{3(2x - 1)^{2}} - \frac{(\frac{-2(2 + 0)}{(2x - 1)^{3}})}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} - 288(\frac{-3(12 + 0)}{(12x - 2)^{4}})\\=&\frac{-8x}{(2x - 1)^{4}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})} + \frac{16x^{2}}{(2x - 1)^{5}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} - \frac{40x}{3(2x - 1)^{4}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} + \frac{16x}{(2x - 1)^{5}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} - \frac{8x}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}(2x - 1)^{4}} - \frac{32x^{3}}{3(2x - 1)^{6}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} + \frac{32x^{2}}{3(2x - 1)^{5}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} - \frac{16x^{2}}{(2x - 1)^{6}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} + \frac{16x^{2}}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}(2x - 1)^{5}} - \frac{8x}{3(2x - 1)^{4}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} + \frac{32x}{3(2x - 1)^{5}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} - \frac{8x}{(2x - 1)^{6}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} - \frac{16x}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}(2x - 1)^{4}} + \frac{16x}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}(2x - 1)^{5}} + \frac{2}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}(2x - 1)^{3}} - \frac{8}{(2x - 1)^{4}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} + \frac{4}{(2x - 1)^{5}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} + \frac{10}{3(2x - 1)^{3}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} - \frac{4}{3(2x - 1)^{6}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} - \frac{4}{(2x - 1)^{4}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})} + \frac{4}{(2x - 1)^{3}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})} + \frac{8}{3(2x - 1)^{5}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} + \frac{4}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}(2x - 1)^{5}} - \frac{8}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}(2x - 1)^{4}} - \frac{4}{3(2x - 1)^{4}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} + \frac{4}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}(2x - 1)^{3}} + \frac{10368}{(12x - 2)^{4}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{-8x}{(2x - 1)^{4}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})} + \frac{16x^{2}}{(2x - 1)^{5}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} - \frac{40x}{3(2x - 1)^{4}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} + \frac{16x}{(2x - 1)^{5}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} - \frac{8x}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}(2x - 1)^{4}} - \frac{32x^{3}}{3(2x - 1)^{6}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} + \frac{32x^{2}}{3(2x - 1)^{5}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} - \frac{16x^{2}}{(2x - 1)^{6}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} + \frac{16x^{2}}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}(2x - 1)^{5}} - \frac{8x}{3(2x - 1)^{4}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} + \frac{32x}{3(2x - 1)^{5}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} - \frac{8x}{(2x - 1)^{6}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} - \frac{16x}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}(2x - 1)^{4}} + \frac{16x}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}(2x - 1)^{5}} + \frac{2}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}(2x - 1)^{3}} - \frac{8}{(2x - 1)^{4}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} + \frac{4}{(2x - 1)^{5}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} + \frac{10}{3(2x - 1)^{3}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} - \frac{4}{3(2x - 1)^{6}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} - \frac{4}{(2x - 1)^{4}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})} + \frac{4}{(2x - 1)^{3}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})} + \frac{8}{3(2x - 1)^{5}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} + \frac{4}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}(2x - 1)^{5}} - \frac{8}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}(2x - 1)^{4}} - \frac{4}{3(2x - 1)^{4}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} + \frac{4}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}(2x - 1)^{3}} + \frac{10368}{(12x - 2)^{4}}\right)}{dx}\\=&\frac{-8(\frac{-4(2 + 0)}{(2x - 1)^{5}})x}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})} - \frac{8(\frac{-(2(\frac{-(2 + 0)}{(2x - 1)^{2}})x + \frac{2}{(2x - 1)} + (\frac{-(2 + 0)}{(2x - 1)^{2}}))}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}})x}{(2x - 1)^{4}} - \frac{8}{(2x - 1)^{4}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})} + \frac{16(\frac{-5(2 + 0)}{(2x - 1)^{6}})x^{2}}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} + \frac{16(\frac{-2(2(\frac{-(2 + 0)}{(2x - 1)^{2}})x + \frac{2}{(2x - 1)} + (\frac{-(2 + 0)}{(2x - 1)^{2}}))}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}})x^{2}}{(2x - 1)^{5}} + \frac{16*2x}{(2x - 1)^{5}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} - \frac{40(\frac{-4(2 + 0)}{(2x - 1)^{5}})x}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} - \frac{40(\frac{-2(2(\frac{-(2 + 0)}{(2x - 1)^{2}})x + \frac{2}{(2x - 1)} + (\frac{-(2 + 0)}{(2x - 1)^{2}}))}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}})x}{3(2x - 1)^{4}} - \frac{40}{3(2x - 1)^{4}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} + \frac{16(\frac{-5(2 + 0)}{(2x - 1)^{6}})x}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} + \frac{16(\frac{-2(2(\frac{-(2 + 0)}{(2x - 1)^{2}})x + \frac{2}{(2x - 1)} + (\frac{-(2 + 0)}{(2x - 1)^{2}}))}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}})x}{(2x - 1)^{5}} + \frac{16}{(2x - 1)^{5}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} - \frac{8(\frac{-2(2(\frac{-(2 + 0)}{(2x - 1)^{2}})x + \frac{2}{(2x - 1)} + (\frac{-(2 + 0)}{(2x - 1)^{2}}))}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}})x}{3(2x - 1)^{4}} - \frac{8(\frac{-4(2 + 0)}{(2x - 1)^{5}})x}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} - \frac{8}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}(2x - 1)^{4}} - \frac{32(\frac{-6(2 + 0)}{(2x - 1)^{7}})x^{3}}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} - \frac{32(\frac{-3(2(\frac{-(2 + 0)}{(2x - 1)^{2}})x + \frac{2}{(2x - 1)} + (\frac{-(2 + 0)}{(2x - 1)^{2}}))}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{4}})x^{3}}{3(2x - 1)^{6}} - \frac{32*3x^{2}}{3(2x - 1)^{6}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} + \frac{32(\frac{-5(2 + 0)}{(2x - 1)^{6}})x^{2}}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} + \frac{32(\frac{-3(2(\frac{-(2 + 0)}{(2x - 1)^{2}})x + \frac{2}{(2x - 1)} + (\frac{-(2 + 0)}{(2x - 1)^{2}}))}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{4}})x^{2}}{3(2x - 1)^{5}} + \frac{32*2x}{3(2x - 1)^{5}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} - \frac{16(\frac{-6(2 + 0)}{(2x - 1)^{7}})x^{2}}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} - \frac{16(\frac{-3(2(\frac{-(2 + 0)}{(2x - 1)^{2}})x + \frac{2}{(2x - 1)} + (\frac{-(2 + 0)}{(2x - 1)^{2}}))}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{4}})x^{2}}{(2x - 1)^{6}} - \frac{16*2x}{(2x - 1)^{6}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} + \frac{16(\frac{-3(2(\frac{-(2 + 0)}{(2x - 1)^{2}})x + \frac{2}{(2x - 1)} + (\frac{-(2 + 0)}{(2x - 1)^{2}}))}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{4}})x^{2}}{3(2x - 1)^{5}} + \frac{16(\frac{-5(2 + 0)}{(2x - 1)^{6}})x^{2}}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} + \frac{16*2x}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}(2x - 1)^{5}} - \frac{8(\frac{-4(2 + 0)}{(2x - 1)^{5}})x}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} - \frac{8(\frac{-3(2(\frac{-(2 + 0)}{(2x - 1)^{2}})x + \frac{2}{(2x - 1)} + (\frac{-(2 + 0)}{(2x - 1)^{2}}))}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{4}})x}{3(2x - 1)^{4}} - \frac{8}{3(2x - 1)^{4}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} + \frac{32(\frac{-5(2 + 0)}{(2x - 1)^{6}})x}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} + \frac{32(\frac{-3(2(\frac{-(2 + 0)}{(2x - 1)^{2}})x + \frac{2}{(2x - 1)} + (\frac{-(2 + 0)}{(2x - 1)^{2}}))}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{4}})x}{3(2x - 1)^{5}} + \frac{32}{3(2x - 1)^{5}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} - \frac{8(\frac{-6(2 + 0)}{(2x - 1)^{7}})x}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} - \frac{8(\frac{-3(2(\frac{-(2 + 0)}{(2x - 1)^{2}})x + \frac{2}{(2x - 1)} + (\frac{-(2 + 0)}{(2x - 1)^{2}}))}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{4}})x}{(2x - 1)^{6}} - \frac{8}{(2x - 1)^{6}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} - \frac{16(\frac{-3(2(\frac{-(2 + 0)}{(2x - 1)^{2}})x + \frac{2}{(2x - 1)} + (\frac{-(2 + 0)}{(2x - 1)^{2}}))}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{4}})x}{3(2x - 1)^{4}} - \frac{16(\frac{-4(2 + 0)}{(2x - 1)^{5}})x}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} - \frac{16}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}(2x - 1)^{4}} + \frac{16(\frac{-3(2(\frac{-(2 + 0)}{(2x - 1)^{2}})x + \frac{2}{(2x - 1)} + (\frac{-(2 + 0)}{(2x - 1)^{2}}))}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{4}})x}{3(2x - 1)^{5}} + \frac{16(\frac{-5(2 + 0)}{(2x - 1)^{6}})x}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} + \frac{16}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}(2x - 1)^{5}} + \frac{2(\frac{-2(2(\frac{-(2 + 0)}{(2x - 1)^{2}})x + \frac{2}{(2x - 1)} + (\frac{-(2 + 0)}{(2x - 1)^{2}}))}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}})}{3(2x - 1)^{3}} + \frac{2(\frac{-3(2 + 0)}{(2x - 1)^{4}})}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} - \frac{8(\frac{-4(2 + 0)}{(2x - 1)^{5}})}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} - \frac{8(\frac{-2(2(\frac{-(2 + 0)}{(2x - 1)^{2}})x + \frac{2}{(2x - 1)} + (\frac{-(2 + 0)}{(2x - 1)^{2}}))}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}})}{(2x - 1)^{4}} + \frac{4(\frac{-5(2 + 0)}{(2x - 1)^{6}})}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} + \frac{4(\frac{-2(2(\frac{-(2 + 0)}{(2x - 1)^{2}})x + \frac{2}{(2x - 1)} + (\frac{-(2 + 0)}{(2x - 1)^{2}}))}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}})}{(2x - 1)^{5}} + \frac{10(\frac{-3(2 + 0)}{(2x - 1)^{4}})}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} + \frac{10(\frac{-2(2(\frac{-(2 + 0)}{(2x - 1)^{2}})x + \frac{2}{(2x - 1)} + (\frac{-(2 + 0)}{(2x - 1)^{2}}))}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}})}{3(2x - 1)^{3}} - \frac{4(\frac{-6(2 + 0)}{(2x - 1)^{7}})}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} - \frac{4(\frac{-3(2(\frac{-(2 + 0)}{(2x - 1)^{2}})x + \frac{2}{(2x - 1)} + (\frac{-(2 + 0)}{(2x - 1)^{2}}))}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{4}})}{3(2x - 1)^{6}} - \frac{4(\frac{-4(2 + 0)}{(2x - 1)^{5}})}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})} - \frac{4(\frac{-(2(\frac{-(2 + 0)}{(2x - 1)^{2}})x + \frac{2}{(2x - 1)} + (\frac{-(2 + 0)}{(2x - 1)^{2}}))}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}})}{(2x - 1)^{4}} + \frac{4(\frac{-3(2 + 0)}{(2x - 1)^{4}})}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})} + \frac{4(\frac{-(2(\frac{-(2 + 0)}{(2x - 1)^{2}})x + \frac{2}{(2x - 1)} + (\frac{-(2 + 0)}{(2x - 1)^{2}}))}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}})}{(2x - 1)^{3}} + \frac{8(\frac{-5(2 + 0)}{(2x - 1)^{6}})}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} + \frac{8(\frac{-3(2(\frac{-(2 + 0)}{(2x - 1)^{2}})x + \frac{2}{(2x - 1)} + (\frac{-(2 + 0)}{(2x - 1)^{2}}))}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{4}})}{3(2x - 1)^{5}} + \frac{4(\frac{-3(2(\frac{-(2 + 0)}{(2x - 1)^{2}})x + \frac{2}{(2x - 1)} + (\frac{-(2 + 0)}{(2x - 1)^{2}}))}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{4}})}{3(2x - 1)^{5}} + \frac{4(\frac{-5(2 + 0)}{(2x - 1)^{6}})}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} - \frac{8(\frac{-3(2(\frac{-(2 + 0)}{(2x - 1)^{2}})x + \frac{2}{(2x - 1)} + (\frac{-(2 + 0)}{(2x - 1)^{2}}))}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{4}})}{3(2x - 1)^{4}} - \frac{8(\frac{-4(2 + 0)}{(2x - 1)^{5}})}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} - \frac{4(\frac{-4(2 + 0)}{(2x - 1)^{5}})}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} - \frac{4(\frac{-3(2(\frac{-(2 + 0)}{(2x - 1)^{2}})x + \frac{2}{(2x - 1)} + (\frac{-(2 + 0)}{(2x - 1)^{2}}))}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{4}})}{3(2x - 1)^{4}} + \frac{4(\frac{-3(2(\frac{-(2 + 0)}{(2x - 1)^{2}})x + \frac{2}{(2x - 1)} + (\frac{-(2 + 0)}{(2x - 1)^{2}}))}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{4}})}{3(2x - 1)^{3}} + \frac{4(\frac{-3(2 + 0)}{(2x - 1)^{4}})}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} + 10368(\frac{-4(12 + 0)}{(12x - 2)^{5}})\\=&\frac{64x}{(2x - 1)^{5}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})} - \frac{192x^{2}}{(2x - 1)^{6}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} - \frac{256x^{3}}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{4}(2x - 1)^{8}} - \frac{192x}{(2x - 1)^{6}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} + \frac{32x}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}(2x - 1)^{5}} + \frac{256x^{3}}{(2x - 1)^{7}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} - \frac{992x^{2}}{3(2x - 1)^{6}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} + \frac{384x^{2}}{(2x - 1)^{7}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} + \frac{160x}{(2x - 1)^{5}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} + \frac{112x}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}(2x - 1)^{5}} - \frac{160x^{2}}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}(2x - 1)^{6}} + \frac{464x}{3(2x - 1)^{5}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} - \frac{1024x}{3(2x - 1)^{6}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} - \frac{96x^{2}}{(2x - 1)^{6}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{4}} - \frac{96x^{2}}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{4}(2x - 1)^{6}} - \frac{128x^{4}}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{4}(2x - 1)^{8}} + \frac{192x^{2}}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{4}(2x - 1)^{7}} - \frac{192x^{2}}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{4}(2x - 1)^{8}} - \frac{128x}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}(2x - 1)^{6}} + \frac{128x^{3}}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{4}(2x - 1)^{7}} + \frac{128x^{3}}{(2x - 1)^{7}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{4}} + \frac{96x}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{4}(2x - 1)^{7}} - \frac{64x}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{4}(2x - 1)^{8}} + \frac{192x^{2}}{(2x - 1)^{7}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{4}} + \frac{16x}{(2x - 1)^{5}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{4}} - \frac{96x}{(2x - 1)^{6}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{4}} + \frac{192x}{(2x - 1)^{7}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} + \frac{96x}{(2x - 1)^{7}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{4}} - \frac{96x}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{4}(2x - 1)^{6}} + \frac{48x}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{4}(2x - 1)^{5}} + \frac{88}{(2x - 1)^{5}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} + \frac{8}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}(2x - 1)^{5}} + \frac{96}{(2x - 1)^{5}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} + \frac{16}{(2x - 1)^{7}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{4}} - \frac{24}{(2x - 1)^{4}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} + \frac{16}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{4}(2x - 1)^{7}} - \frac{8}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}(2x - 1)^{4}} + \frac{32}{(2x - 1)^{7}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} - \frac{24}{(2x - 1)^{6}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{4}} - \frac{136}{3(2x - 1)^{4}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} - \frac{24}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{4}(2x - 1)^{6}} - \frac{8}{3(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}(2x - 1)^{4}} - \frac{96}{(2x - 1)^{6}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{3}} + \frac{8}{(2x - 1)^{5}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{4}} + \frac{32}{(2x - 1)^{5}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})} + \frac{24}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{4}(2x - 1)^{5}} - \frac{32}{(2x - 1)^{4}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})} - \frac{48}{(2x - 1)^{6}(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{2}} - \frac{8}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{4}(2x - 1)^{4}} - \frac{8}{(\frac{2x}{(2x - 1)} + \frac{1}{(2x - 1)})^{4}(2x - 1)^{8}} - \frac{497664}{(12x - 2)^{5}}\\ \end{split}\end{equation} \]

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