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。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{{3}^{x}}{arctan({x}^{2} - 1)} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{{3}^{x}}{arctan(x^{2} - 1)}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{{3}^{x}}{arctan(x^{2} - 1)}\right)}{dx}\\=&\frac{({3}^{x}((1)ln(3) + \frac{(x)(0)}{(3)}))}{arctan(x^{2} - 1)} + {3}^{x}(\frac{-(2x + 0)}{arctan^{2}(x^{2} - 1)(1 + (x^{2} - 1)^{2})})\\=&\frac{{3}^{x}ln(3)}{arctan(x^{2} - 1)} - \frac{2x{3}^{x}}{(x^{4} - 2x^{2} + 2)arctan^{2}(x^{2} - 1)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{{3}^{x}ln(3)}{arctan(x^{2} - 1)} - \frac{2x{3}^{x}}{(x^{4} - 2x^{2} + 2)arctan^{2}(x^{2} - 1)}\right)}{dx}\\=&\frac{({3}^{x}((1)ln(3) + \frac{(x)(0)}{(3)}))ln(3)}{arctan(x^{2} - 1)} + \frac{{3}^{x}*0}{(3)arctan(x^{2} - 1)} + {3}^{x}ln(3)(\frac{-(2x + 0)}{arctan^{2}(x^{2} - 1)(1 + (x^{2} - 1)^{2})}) - \frac{2(\frac{-(4x^{3} - 2*2x + 0)}{(x^{4} - 2x^{2} + 2)^{2}})x{3}^{x}}{arctan^{2}(x^{2} - 1)} - \frac{2 * {3}^{x}}{(x^{4} - 2x^{2} + 2)arctan^{2}(x^{2} - 1)} - \frac{2x({3}^{x}((1)ln(3) + \frac{(x)(0)}{(3)}))}{(x^{4} - 2x^{2} + 2)arctan^{2}(x^{2} - 1)} - \frac{2x{3}^{x}(\frac{-2(2x + 0)}{arctan^{3}(x^{2} - 1)(1 + (x^{2} - 1)^{2})})}{(x^{4} - 2x^{2} + 2)}\\=&\frac{{3}^{x}ln^{2}(3)}{arctan(x^{2} - 1)} - \frac{4x{3}^{x}ln(3)}{(x^{4} - 2x^{2} + 2)arctan^{2}(x^{2} - 1)} + \frac{8x^{4}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{2}arctan^{2}(x^{2} - 1)} - \frac{8x^{2}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{2}arctan^{2}(x^{2} - 1)} - \frac{2 * {3}^{x}}{(x^{4} - 2x^{2} + 2)arctan^{2}(x^{2} - 1)} + \frac{8x^{2}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{2}arctan^{3}(x^{2} - 1)}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{{3}^{x}ln^{2}(3)}{arctan(x^{2} - 1)} - \frac{4x{3}^{x}ln(3)}{(x^{4} - 2x^{2} + 2)arctan^{2}(x^{2} - 1)} + \frac{8x^{4}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{2}arctan^{2}(x^{2} - 1)} - \frac{8x^{2}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{2}arctan^{2}(x^{2} - 1)} - \frac{2 * {3}^{x}}{(x^{4} - 2x^{2} + 2)arctan^{2}(x^{2} - 1)} + \frac{8x^{2}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{2}arctan^{3}(x^{2} - 1)}\right)}{dx}\\=&\frac{({3}^{x}((1)ln(3) + \frac{(x)(0)}{(3)}))ln^{2}(3)}{arctan(x^{2} - 1)} + \frac{{3}^{x}*2ln(3)*0}{(3)arctan(x^{2} - 1)} + {3}^{x}ln^{2}(3)(\frac{-(2x + 0)}{arctan^{2}(x^{2} - 1)(1 + (x^{2} - 1)^{2})}) - \frac{4(\frac{-(4x^{3} - 2*2x + 0)}{(x^{4} - 2x^{2} + 2)^{2}})x{3}^{x}ln(3)}{arctan^{2}(x^{2} - 1)} - \frac{4 * {3}^{x}ln(3)}{(x^{4} - 2x^{2} + 2)arctan^{2}(x^{2} - 1)} - \frac{4x({3}^{x}((1)ln(3) + \frac{(x)(0)}{(3)}))ln(3)}{(x^{4} - 2x^{2} + 2)arctan^{2}(x^{2} - 1)} - \frac{4x{3}^{x}*0}{(x^{4} - 2x^{2} + 2)(3)arctan^{2}(x^{2} - 1)} - \frac{4x{3}^{x}ln(3)(\frac{-2(2x + 0)}{arctan^{3}(x^{2} - 1)(1 + (x^{2} - 1)^{2})})}{(x^{4} - 2x^{2} + 2)} + \frac{8(\frac{-2(4x^{3} - 2*2x + 0)}{(x^{4} - 2x^{2} + 2)^{3}})x^{4}{3}^{x}}{arctan^{2}(x^{2} - 1)} + \frac{8*4x^{3}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{2}arctan^{2}(x^{2} - 1)} + \frac{8x^{4}({3}^{x}((1)ln(3) + \frac{(x)(0)}{(3)}))}{(x^{4} - 2x^{2} + 2)^{2}arctan^{2}(x^{2} - 1)} + \frac{8x^{4}{3}^{x}(\frac{-2(2x + 0)}{arctan^{3}(x^{2} - 1)(1 + (x^{2} - 1)^{2})})}{(x^{4} - 2x^{2} + 2)^{2}} - \frac{8(\frac{-2(4x^{3} - 2*2x + 0)}{(x^{4} - 2x^{2} + 2)^{3}})x^{2}{3}^{x}}{arctan^{2}(x^{2} - 1)} - \frac{8*2x{3}^{x}}{(x^{4} - 2x^{2} + 2)^{2}arctan^{2}(x^{2} - 1)} - \frac{8x^{2}({3}^{x}((1)ln(3) + \frac{(x)(0)}{(3)}))}{(x^{4} - 2x^{2} + 2)^{2}arctan^{2}(x^{2} - 1)} - \frac{8x^{2}{3}^{x}(\frac{-2(2x + 0)}{arctan^{3}(x^{2} - 1)(1 + (x^{2} - 1)^{2})})}{(x^{4} - 2x^{2} + 2)^{2}} - \frac{2(\frac{-(4x^{3} - 2*2x + 0)}{(x^{4} - 2x^{2} + 2)^{2}}){3}^{x}}{arctan^{2}(x^{2} - 1)} - \frac{2({3}^{x}((1)ln(3) + \frac{(x)(0)}{(3)}))}{(x^{4} - 2x^{2} + 2)arctan^{2}(x^{2} - 1)} - \frac{2 * {3}^{x}(\frac{-2(2x + 0)}{arctan^{3}(x^{2} - 1)(1 + (x^{2} - 1)^{2})})}{(x^{4} - 2x^{2} + 2)} + \frac{8(\frac{-2(4x^{3} - 2*2x + 0)}{(x^{4} - 2x^{2} + 2)^{3}})x^{2}{3}^{x}}{arctan^{3}(x^{2} - 1)} + \frac{8*2x{3}^{x}}{(x^{4} - 2x^{2} + 2)^{2}arctan^{3}(x^{2} - 1)} + \frac{8x^{2}({3}^{x}((1)ln(3) + \frac{(x)(0)}{(3)}))}{(x^{4} - 2x^{2} + 2)^{2}arctan^{3}(x^{2} - 1)} + \frac{8x^{2}{3}^{x}(\frac{-3(2x + 0)}{arctan^{4}(x^{2} - 1)(1 + (x^{2} - 1)^{2})})}{(x^{4} - 2x^{2} + 2)^{2}}\\=&\frac{{3}^{x}ln^{3}(3)}{arctan(x^{2} - 1)} - \frac{6x{3}^{x}ln^{2}(3)}{(x^{4} - 2x^{2} + 2)arctan^{2}(x^{2} - 1)} + \frac{24x^{4}{3}^{x}ln(3)}{(x^{4} - 2x^{2} + 2)^{2}arctan^{2}(x^{2} - 1)} - \frac{24x^{2}{3}^{x}ln(3)}{(x^{4} - 2x^{2} + 2)^{2}arctan^{2}(x^{2} - 1)} - \frac{6 * {3}^{x}ln(3)}{(x^{4} - 2x^{2} + 2)arctan^{2}(x^{2} - 1)} + \frac{24x^{2}{3}^{x}ln(3)}{(x^{4} - 2x^{2} + 2)^{2}arctan^{3}(x^{2} - 1)} - \frac{64x^{7}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{3}arctan^{2}(x^{2} - 1)} + \frac{128x^{5}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{3}arctan^{2}(x^{2} - 1)} + \frac{40x^{3}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{2}arctan^{2}(x^{2} - 1)} - \frac{96x^{5}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{3}arctan^{3}(x^{2} - 1)} - \frac{64x^{3}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{3}arctan^{2}(x^{2} - 1)} - \frac{24x{3}^{x}}{(x^{4} - 2x^{2} + 2)^{2}arctan^{2}(x^{2} - 1)} + \frac{96x^{3}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{3}arctan^{3}(x^{2} - 1)} + \frac{24x{3}^{x}}{(x^{4} - 2x^{2} + 2)^{2}arctan^{3}(x^{2} - 1)} - \frac{48x^{3}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{3}arctan^{4}(x^{2} - 1)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{{3}^{x}ln^{3}(3)}{arctan(x^{2} - 1)} - \frac{6x{3}^{x}ln^{2}(3)}{(x^{4} - 2x^{2} + 2)arctan^{2}(x^{2} - 1)} + \frac{24x^{4}{3}^{x}ln(3)}{(x^{4} - 2x^{2} + 2)^{2}arctan^{2}(x^{2} - 1)} - \frac{24x^{2}{3}^{x}ln(3)}{(x^{4} - 2x^{2} + 2)^{2}arctan^{2}(x^{2} - 1)} - \frac{6 * {3}^{x}ln(3)}{(x^{4} - 2x^{2} + 2)arctan^{2}(x^{2} - 1)} + \frac{24x^{2}{3}^{x}ln(3)}{(x^{4} - 2x^{2} + 2)^{2}arctan^{3}(x^{2} - 1)} - \frac{64x^{7}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{3}arctan^{2}(x^{2} - 1)} + \frac{128x^{5}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{3}arctan^{2}(x^{2} - 1)} + \frac{40x^{3}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{2}arctan^{2}(x^{2} - 1)} - \frac{96x^{5}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{3}arctan^{3}(x^{2} - 1)} - \frac{64x^{3}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{3}arctan^{2}(x^{2} - 1)} - \frac{24x{3}^{x}}{(x^{4} - 2x^{2} + 2)^{2}arctan^{2}(x^{2} - 1)} + \frac{96x^{3}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{3}arctan^{3}(x^{2} - 1)} + \frac{24x{3}^{x}}{(x^{4} - 2x^{2} + 2)^{2}arctan^{3}(x^{2} - 1)} - \frac{48x^{3}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{3}arctan^{4}(x^{2} - 1)}\right)}{dx}\\=&\frac{({3}^{x}((1)ln(3) + \frac{(x)(0)}{(3)}))ln^{3}(3)}{arctan(x^{2} - 1)} + \frac{{3}^{x}*3ln^{2}(3)*0}{(3)arctan(x^{2} - 1)} + {3}^{x}ln^{3}(3)(\frac{-(2x + 0)}{arctan^{2}(x^{2} - 1)(1 + (x^{2} - 1)^{2})}) - \frac{6(\frac{-(4x^{3} - 2*2x + 0)}{(x^{4} - 2x^{2} + 2)^{2}})x{3}^{x}ln^{2}(3)}{arctan^{2}(x^{2} - 1)} - \frac{6 * {3}^{x}ln^{2}(3)}{(x^{4} - 2x^{2} + 2)arctan^{2}(x^{2} - 1)} - \frac{6x({3}^{x}((1)ln(3) + \frac{(x)(0)}{(3)}))ln^{2}(3)}{(x^{4} - 2x^{2} + 2)arctan^{2}(x^{2} - 1)} - \frac{6x{3}^{x}*2ln(3)*0}{(x^{4} - 2x^{2} + 2)(3)arctan^{2}(x^{2} - 1)} - \frac{6x{3}^{x}ln^{2}(3)(\frac{-2(2x + 0)}{arctan^{3}(x^{2} - 1)(1 + (x^{2} - 1)^{2})})}{(x^{4} - 2x^{2} + 2)} + \frac{24(\frac{-2(4x^{3} - 2*2x + 0)}{(x^{4} - 2x^{2} + 2)^{3}})x^{4}{3}^{x}ln(3)}{arctan^{2}(x^{2} - 1)} + \frac{24*4x^{3}{3}^{x}ln(3)}{(x^{4} - 2x^{2} + 2)^{2}arctan^{2}(x^{2} - 1)} + \frac{24x^{4}({3}^{x}((1)ln(3) + \frac{(x)(0)}{(3)}))ln(3)}{(x^{4} - 2x^{2} + 2)^{2}arctan^{2}(x^{2} - 1)} + \frac{24x^{4}{3}^{x}*0}{(x^{4} - 2x^{2} + 2)^{2}(3)arctan^{2}(x^{2} - 1)} + \frac{24x^{4}{3}^{x}ln(3)(\frac{-2(2x + 0)}{arctan^{3}(x^{2} - 1)(1 + (x^{2} - 1)^{2})})}{(x^{4} - 2x^{2} + 2)^{2}} - \frac{24(\frac{-2(4x^{3} - 2*2x + 0)}{(x^{4} - 2x^{2} + 2)^{3}})x^{2}{3}^{x}ln(3)}{arctan^{2}(x^{2} - 1)} - \frac{24*2x{3}^{x}ln(3)}{(x^{4} - 2x^{2} + 2)^{2}arctan^{2}(x^{2} - 1)} - \frac{24x^{2}({3}^{x}((1)ln(3) + \frac{(x)(0)}{(3)}))ln(3)}{(x^{4} - 2x^{2} + 2)^{2}arctan^{2}(x^{2} - 1)} - \frac{24x^{2}{3}^{x}*0}{(x^{4} - 2x^{2} + 2)^{2}(3)arctan^{2}(x^{2} - 1)} - \frac{24x^{2}{3}^{x}ln(3)(\frac{-2(2x + 0)}{arctan^{3}(x^{2} - 1)(1 + (x^{2} - 1)^{2})})}{(x^{4} - 2x^{2} + 2)^{2}} - \frac{6(\frac{-(4x^{3} - 2*2x + 0)}{(x^{4} - 2x^{2} + 2)^{2}}){3}^{x}ln(3)}{arctan^{2}(x^{2} - 1)} - \frac{6({3}^{x}((1)ln(3) + \frac{(x)(0)}{(3)}))ln(3)}{(x^{4} - 2x^{2} + 2)arctan^{2}(x^{2} - 1)} - \frac{6 * {3}^{x}*0}{(x^{4} - 2x^{2} + 2)(3)arctan^{2}(x^{2} - 1)} - \frac{6 * {3}^{x}ln(3)(\frac{-2(2x + 0)}{arctan^{3}(x^{2} - 1)(1 + (x^{2} - 1)^{2})})}{(x^{4} - 2x^{2} + 2)} + \frac{24(\frac{-2(4x^{3} - 2*2x + 0)}{(x^{4} - 2x^{2} + 2)^{3}})x^{2}{3}^{x}ln(3)}{arctan^{3}(x^{2} - 1)} + \frac{24*2x{3}^{x}ln(3)}{(x^{4} - 2x^{2} + 2)^{2}arctan^{3}(x^{2} - 1)} + \frac{24x^{2}({3}^{x}((1)ln(3) + \frac{(x)(0)}{(3)}))ln(3)}{(x^{4} - 2x^{2} + 2)^{2}arctan^{3}(x^{2} - 1)} + \frac{24x^{2}{3}^{x}*0}{(x^{4} - 2x^{2} + 2)^{2}(3)arctan^{3}(x^{2} - 1)} + \frac{24x^{2}{3}^{x}ln(3)(\frac{-3(2x + 0)}{arctan^{4}(x^{2} - 1)(1 + (x^{2} - 1)^{2})})}{(x^{4} - 2x^{2} + 2)^{2}} - \frac{64(\frac{-3(4x^{3} - 2*2x + 0)}{(x^{4} - 2x^{2} + 2)^{4}})x^{7}{3}^{x}}{arctan^{2}(x^{2} - 1)} - \frac{64*7x^{6}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{3}arctan^{2}(x^{2} - 1)} - \frac{64x^{7}({3}^{x}((1)ln(3) + \frac{(x)(0)}{(3)}))}{(x^{4} - 2x^{2} + 2)^{3}arctan^{2}(x^{2} - 1)} - \frac{64x^{7}{3}^{x}(\frac{-2(2x + 0)}{arctan^{3}(x^{2} - 1)(1 + (x^{2} - 1)^{2})})}{(x^{4} - 2x^{2} + 2)^{3}} + \frac{128(\frac{-3(4x^{3} - 2*2x + 0)}{(x^{4} - 2x^{2} + 2)^{4}})x^{5}{3}^{x}}{arctan^{2}(x^{2} - 1)} + \frac{128*5x^{4}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{3}arctan^{2}(x^{2} - 1)} + \frac{128x^{5}({3}^{x}((1)ln(3) + \frac{(x)(0)}{(3)}))}{(x^{4} - 2x^{2} + 2)^{3}arctan^{2}(x^{2} - 1)} + \frac{128x^{5}{3}^{x}(\frac{-2(2x + 0)}{arctan^{3}(x^{2} - 1)(1 + (x^{2} - 1)^{2})})}{(x^{4} - 2x^{2} + 2)^{3}} + \frac{40(\frac{-2(4x^{3} - 2*2x + 0)}{(x^{4} - 2x^{2} + 2)^{3}})x^{3}{3}^{x}}{arctan^{2}(x^{2} - 1)} + \frac{40*3x^{2}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{2}arctan^{2}(x^{2} - 1)} + \frac{40x^{3}({3}^{x}((1)ln(3) + \frac{(x)(0)}{(3)}))}{(x^{4} - 2x^{2} + 2)^{2}arctan^{2}(x^{2} - 1)} + \frac{40x^{3}{3}^{x}(\frac{-2(2x + 0)}{arctan^{3}(x^{2} - 1)(1 + (x^{2} - 1)^{2})})}{(x^{4} - 2x^{2} + 2)^{2}} - \frac{96(\frac{-3(4x^{3} - 2*2x + 0)}{(x^{4} - 2x^{2} + 2)^{4}})x^{5}{3}^{x}}{arctan^{3}(x^{2} - 1)} - \frac{96*5x^{4}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{3}arctan^{3}(x^{2} - 1)} - \frac{96x^{5}({3}^{x}((1)ln(3) + \frac{(x)(0)}{(3)}))}{(x^{4} - 2x^{2} + 2)^{3}arctan^{3}(x^{2} - 1)} - \frac{96x^{5}{3}^{x}(\frac{-3(2x + 0)}{arctan^{4}(x^{2} - 1)(1 + (x^{2} - 1)^{2})})}{(x^{4} - 2x^{2} + 2)^{3}} - \frac{64(\frac{-3(4x^{3} - 2*2x + 0)}{(x^{4} - 2x^{2} + 2)^{4}})x^{3}{3}^{x}}{arctan^{2}(x^{2} - 1)} - \frac{64*3x^{2}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{3}arctan^{2}(x^{2} - 1)} - \frac{64x^{3}({3}^{x}((1)ln(3) + \frac{(x)(0)}{(3)}))}{(x^{4} - 2x^{2} + 2)^{3}arctan^{2}(x^{2} - 1)} - \frac{64x^{3}{3}^{x}(\frac{-2(2x + 0)}{arctan^{3}(x^{2} - 1)(1 + (x^{2} - 1)^{2})})}{(x^{4} - 2x^{2} + 2)^{3}} - \frac{24(\frac{-2(4x^{3} - 2*2x + 0)}{(x^{4} - 2x^{2} + 2)^{3}})x{3}^{x}}{arctan^{2}(x^{2} - 1)} - \frac{24 * {3}^{x}}{(x^{4} - 2x^{2} + 2)^{2}arctan^{2}(x^{2} - 1)} - \frac{24x({3}^{x}((1)ln(3) + \frac{(x)(0)}{(3)}))}{(x^{4} - 2x^{2} + 2)^{2}arctan^{2}(x^{2} - 1)} - \frac{24x{3}^{x}(\frac{-2(2x + 0)}{arctan^{3}(x^{2} - 1)(1 + (x^{2} - 1)^{2})})}{(x^{4} - 2x^{2} + 2)^{2}} + \frac{96(\frac{-3(4x^{3} - 2*2x + 0)}{(x^{4} - 2x^{2} + 2)^{4}})x^{3}{3}^{x}}{arctan^{3}(x^{2} - 1)} + \frac{96*3x^{2}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{3}arctan^{3}(x^{2} - 1)} + \frac{96x^{3}({3}^{x}((1)ln(3) + \frac{(x)(0)}{(3)}))}{(x^{4} - 2x^{2} + 2)^{3}arctan^{3}(x^{2} - 1)} + \frac{96x^{3}{3}^{x}(\frac{-3(2x + 0)}{arctan^{4}(x^{2} - 1)(1 + (x^{2} - 1)^{2})})}{(x^{4} - 2x^{2} + 2)^{3}} + \frac{24(\frac{-2(4x^{3} - 2*2x + 0)}{(x^{4} - 2x^{2} + 2)^{3}})x{3}^{x}}{arctan^{3}(x^{2} - 1)} + \frac{24 * {3}^{x}}{(x^{4} - 2x^{2} + 2)^{2}arctan^{3}(x^{2} - 1)} + \frac{24x({3}^{x}((1)ln(3) + \frac{(x)(0)}{(3)}))}{(x^{4} - 2x^{2} + 2)^{2}arctan^{3}(x^{2} - 1)} + \frac{24x{3}^{x}(\frac{-3(2x + 0)}{arctan^{4}(x^{2} - 1)(1 + (x^{2} - 1)^{2})})}{(x^{4} - 2x^{2} + 2)^{2}} - \frac{48(\frac{-3(4x^{3} - 2*2x + 0)}{(x^{4} - 2x^{2} + 2)^{4}})x^{3}{3}^{x}}{arctan^{4}(x^{2} - 1)} - \frac{48*3x^{2}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{3}arctan^{4}(x^{2} - 1)} - \frac{48x^{3}({3}^{x}((1)ln(3) + \frac{(x)(0)}{(3)}))}{(x^{4} - 2x^{2} + 2)^{3}arctan^{4}(x^{2} - 1)} - \frac{48x^{3}{3}^{x}(\frac{-4(2x + 0)}{arctan^{5}(x^{2} - 1)(1 + (x^{2} - 1)^{2})})}{(x^{4} - 2x^{2} + 2)^{3}}\\=&\frac{{3}^{x}ln^{4}(3)}{arctan(x^{2} - 1)} - \frac{8x{3}^{x}ln^{3}(3)}{(x^{4} - 2x^{2} + 2)arctan^{2}(x^{2} - 1)} + \frac{48x^{4}{3}^{x}ln^{2}(3)}{(x^{4} - 2x^{2} + 2)^{2}arctan^{2}(x^{2} - 1)} - \frac{48x^{2}{3}^{x}ln^{2}(3)}{(x^{4} - 2x^{2} + 2)^{2}arctan^{2}(x^{2} - 1)} - \frac{12 * {3}^{x}ln^{2}(3)}{(x^{4} - 2x^{2} + 2)arctan^{2}(x^{2} - 1)} + \frac{48x^{2}{3}^{x}ln^{2}(3)}{(x^{4} - 2x^{2} + 2)^{2}arctan^{3}(x^{2} - 1)} - \frac{256x^{7}{3}^{x}ln(3)}{(x^{4} - 2x^{2} + 2)^{3}arctan^{2}(x^{2} - 1)} + \frac{512x^{5}{3}^{x}ln(3)}{(x^{4} - 2x^{2} + 2)^{3}arctan^{2}(x^{2} - 1)} + \frac{160x^{3}{3}^{x}ln(3)}{(x^{4} - 2x^{2} + 2)^{2}arctan^{2}(x^{2} - 1)} - \frac{384x^{5}{3}^{x}ln(3)}{(x^{4} - 2x^{2} + 2)^{3}arctan^{3}(x^{2} - 1)} - \frac{256x^{3}{3}^{x}ln(3)}{(x^{4} - 2x^{2} + 2)^{3}arctan^{2}(x^{2} - 1)} - \frac{96x{3}^{x}ln(3)}{(x^{4} - 2x^{2} + 2)^{2}arctan^{2}(x^{2} - 1)} + \frac{120x^{2}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{2}arctan^{2}(x^{2} - 1)} + \frac{384x^{3}{3}^{x}ln(3)}{(x^{4} - 2x^{2} + 2)^{3}arctan^{3}(x^{2} - 1)} + \frac{96x{3}^{x}ln(3)}{(x^{4} - 2x^{2} + 2)^{2}arctan^{3}(x^{2} - 1)} - \frac{192x^{3}{3}^{x}ln(3)}{(x^{4} - 2x^{2} + 2)^{3}arctan^{4}(x^{2} - 1)} + \frac{768x^{10}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{4}arctan^{2}(x^{2} - 1)} - \frac{2304x^{8}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{4}arctan^{2}(x^{2} - 1)} - \frac{768x^{6}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{3}arctan^{2}(x^{2} - 1)} + \frac{1408x^{8}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{4}arctan^{3}(x^{2} - 1)} + \frac{2304x^{6}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{4}arctan^{2}(x^{2} - 1)} + \frac{1152x^{4}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{3}arctan^{2}(x^{2} - 1)} - \frac{2816x^{6}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{4}arctan^{3}(x^{2} - 1)} - \frac{832x^{4}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{3}arctan^{3}(x^{2} - 1)} + \frac{1152x^{6}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{4}arctan^{4}(x^{2} - 1)} - \frac{768x^{4}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{4}arctan^{2}(x^{2} - 1)} - \frac{384x^{2}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{3}arctan^{2}(x^{2} - 1)} + \frac{1408x^{4}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{4}arctan^{3}(x^{2} - 1)} - \frac{24 * {3}^{x}}{(x^{4} - 2x^{2} + 2)^{2}arctan^{2}(x^{2} - 1)} + \frac{576x^{2}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{3}arctan^{3}(x^{2} - 1)} - \frac{1152x^{4}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{4}arctan^{4}(x^{2} - 1)} + \frac{24 * {3}^{x}}{(x^{4} - 2x^{2} + 2)^{2}arctan^{3}(x^{2} - 1)} - \frac{288x^{2}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{3}arctan^{4}(x^{2} - 1)} + \frac{384x^{4}{3}^{x}}{(x^{4} - 2x^{2} + 2)^{4}arctan^{5}(x^{2} - 1)}\\ \end{split}\end{equation} \]

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