¿Cómo vas a descomponer esta cot(4*x)^2*(-12-12*cot(4*x)^2)*acot(2*x^3)-6*x^2*cot(4*x)^3/(1+4*x^6) expresión en fracciones?

                     /   3\                                                     /   3\                                                                                                2                                                                                               8        /   3\                                                             4        /   3\                                                              12        /   3\                                                                                       2    4                                                                                                                      2    8                                                                          4        /   3\                         8        /   3\                                            16        /   3\                                                                                      2    12                                                                                                                       2    2                                                                                                                     2    10                                                                          2        /   3\                          6        /   3\                                            2        /   3\                                                             14        /   3\                                                                                        2    6                                                                                             6        /   3\                                                             10        /   3\                         
              12*acot\2*x /                                              12*acot\2*x /                                                                                             6*x                                                                                       20808*cot (x)*acot\2*x /                                                     2640*cot (x)*acot\2*x /                                                      2640*cot  (x)*acot\2*x /                                                                                  666*x *cot (x)                                                                                                              666*x *cot (x)                                                                456*cot (x)*acot\2*x /                   12*cot (x)*acot\2*x /                                      12*cot  (x)*acot\2*x /                                                                                   6*x *cot  (x)                                                                                                               108*x *cot (x)                                                                                                             108*x *cot  (x)                                                                144*cot (x)*acot\2*x /                   144*cot (x)*acot\2*x /                                     288*cot (x)*acot\2*x /                                                      288*cot  (x)*acot\2*x /                                                                                  1512*x *cot (x)                                                                                 11232*cot (x)*acot\2*x /                                                    11232*cot  (x)*acot\2*x /                         
- -------------------------------------- - -------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------- - -------------------------------------------------------------------------- - -------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------- - -------------------------------------- - -------------------------------------- - -------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------- + -------------------------------------- + -------------------------------------- + -------------------------------------------------------------------------- + -------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------- + --------------------------------------------------------------------------
          4            2            6                6              10             4             12              8               7            3            9             5           6    7           6    3           6    9           6    5                6              10             4             12              8                6              10             4             12              8                6              10             4             12              8               7            3            9             5           6    7           6    3           6    9           6    5               7            3            9             5           6    7           6    3           6    9           6    5              4            2            6              4            2            6                6              10             4             12              8               7            3            9             5           6    7           6    3           6    9           6    5               7            3            9             5           6    7           6    3           6    9           6    5               7            3            9             5           6    7           6    3           6    9           6    5              4            2            6              4            2            6                6              10             4             12              8                6              10             4             12              8               7            3            9             5           6    7           6    3           6    9           6    5                6              10             4             12              8                6              10             4             12              8   
  - 32*cot (x) + 16*cot (x) + 16*cot (x)   - 1024*cot (x) - 1024*cot  (x) + 256*cot (x) + 256*cot  (x) + 1536*cot (x)   - 192*cot (x) - 64*cot (x) + 64*cot (x) + 192*cot (x) - 768*x *cot (x) - 256*x *cot (x) + 256*x *cot (x) + 768*x *cot (x)   - 1024*cot (x) - 1024*cot  (x) + 256*cot (x) + 256*cot  (x) + 1536*cot (x)   - 1024*cot (x) - 1024*cot  (x) + 256*cot (x) + 256*cot  (x) + 1536*cot (x)   - 1024*cot (x) - 1024*cot  (x) + 256*cot (x) + 256*cot  (x) + 1536*cot (x)   - 192*cot (x) - 64*cot (x) + 64*cot (x) + 192*cot (x) - 768*x *cot (x) - 256*x *cot (x) + 256*x *cot (x) + 768*x *cot (x)   - 192*cot (x) - 64*cot (x) + 64*cot (x) + 192*cot (x) - 768*x *cot (x) - 256*x *cot (x) + 256*x *cot (x) + 768*x *cot (x)   - 32*cot (x) + 16*cot (x) + 16*cot (x)   - 32*cot (x) + 16*cot (x) + 16*cot (x)   - 1024*cot (x) - 1024*cot  (x) + 256*cot (x) + 256*cot  (x) + 1536*cot (x)   - 192*cot (x) - 64*cot (x) + 64*cot (x) + 192*cot (x) - 768*x *cot (x) - 256*x *cot (x) + 256*x *cot (x) + 768*x *cot (x)   - 192*cot (x) - 64*cot (x) + 64*cot (x) + 192*cot (x) - 768*x *cot (x) - 256*x *cot (x) + 256*x *cot (x) + 768*x *cot (x)   - 192*cot (x) - 64*cot (x) + 64*cot (x) + 192*cot (x) - 768*x *cot (x) - 256*x *cot (x) + 256*x *cot (x) + 768*x *cot (x)   - 32*cot (x) + 16*cot (x) + 16*cot (x)   - 32*cot (x) + 16*cot (x) + 16*cot (x)   - 1024*cot (x) - 1024*cot  (x) + 256*cot (x) + 256*cot  (x) + 1536*cot (x)   - 1024*cot (x) - 1024*cot  (x) + 256*cot (x) + 256*cot  (x) + 1536*cot (x)   - 192*cot (x) - 64*cot (x) + 64*cot (x) + 192*cot (x) - 768*x *cot (x) - 256*x *cot (x) + 256*x *cot (x) + 768*x *cot (x)   - 1024*cot (x) - 1024*cot  (x) + 256*cot (x) + 256*cot  (x) + 1536*cot (x)   - 1024*cot (x) - 1024*cot  (x) + 256*cot (x) + 256*cot  (x) + 1536*cot (x)

$$- \frac{6 x^{2} \cot^{12}{\left(x \right)}}{256 x^{6} \cot^{9}{\left(x \right)} - 768 x^{6} \cot^{7}{\left(x \right)} + 768 x^{6} \cot^{5}{\left(x \right)} - 256 x^{6} \cot^{3}{\left(x \right)} + 64 \cot^{9}{\left(x \right)} - 192 \cot^{7}{\left(x \right)} + 192 \cot^{5}{\left(x \right)} - 64 \cot^{3}{\left(x \right)}} + \frac{108 x^{2} \cot^{10}{\left(x \right)}}{256 x^{6} \cot^{9}{\left(x \right)} - 768 x^{6} \cot^{7}{\left(x \right)} + 768 x^{6} \cot^{5}{\left(x \right)} - 256 x^{6} \cot^{3}{\left(x \right)} + 64 \cot^{9}{\left(x \right)} - 192 \cot^{7}{\left(x \right)} + 192 \cot^{5}{\left(x \right)} - 64 \cot^{3}{\left(x \right)}} - \frac{666 x^{2} \cot^{8}{\left(x \right)}}{256 x^{6} \cot^{9}{\left(x \right)} - 768 x^{6} \cot^{7}{\left(x \right)} + 768 x^{6} \cot^{5}{\left(x \right)} - 256 x^{6} \cot^{3}{\left(x \right)} + 64 \cot^{9}{\left(x \right)} - 192 \cot^{7}{\left(x \right)} + 192 \cot^{5}{\left(x \right)} - 64 \cot^{3}{\left(x \right)}} + \frac{1512 x^{2} \cot^{6}{\left(x \right)}}{256 x^{6} \cot^{9}{\left(x \right)} - 768 x^{6} \cot^{7}{\left(x \right)} + 768 x^{6} \cot^{5}{\left(x \right)} - 256 x^{6} \cot^{3}{\left(x \right)} + 64 \cot^{9}{\left(x \right)} - 192 \cot^{7}{\left(x \right)} + 192 \cot^{5}{\left(x \right)} - 64 \cot^{3}{\left(x \right)}} - \frac{666 x^{2} \cot^{4}{\left(x \right)}}{256 x^{6} \cot^{9}{\left(x \right)} - 768 x^{6} \cot^{7}{\left(x \right)} + 768 x^{6} \cot^{5}{\left(x \right)} - 256 x^{6} \cot^{3}{\left(x \right)} + 64 \cot^{9}{\left(x \right)} - 192 \cot^{7}{\left(x \right)} + 192 \cot^{5}{\left(x \right)} - 64 \cot^{3}{\left(x \right)}} + \frac{108 x^{2} \cot^{2}{\left(x \right)}}{256 x^{6} \cot^{9}{\left(x \right)} - 768 x^{6} \cot^{7}{\left(x \right)} + 768 x^{6} \cot^{5}{\left(x \right)} - 256 x^{6} \cot^{3}{\left(x \right)} + 64 \cot^{9}{\left(x \right)} - 192 \cot^{7}{\left(x \right)} + 192 \cot^{5}{\left(x \right)} - 64 \cot^{3}{\left(x \right)}} - \frac{6 x^{2}}{256 x^{6} \cot^{9}{\left(x \right)} - 768 x^{6} \cot^{7}{\left(x \right)} + 768 x^{6} \cot^{5}{\left(x \right)} - 256 x^{6} \cot^{3}{\left(x \right)} + 64 \cot^{9}{\left(x \right)} - 192 \cot^{7}{\left(x \right)} + 192 \cot^{5}{\left(x \right)} - 64 \cot^{3}{\left(x \right)}} - \frac{12 \cot^{16}{\left(x \right)} \operatorname{acot}{\left(2 x^{3} \right)}}{256 \cot^{12}{\left(x \right)} - 1024 \cot^{10}{\left(x \right)} + 1536 \cot^{8}{\left(x \right)} - 1024 \cot^{6}{\left(x \right)} + 256 \cot^{4}{\left(x \right)}} + \frac{288 \cot^{14}{\left(x \right)} \operatorname{acot}{\left(2 x^{3} \right)}}{256 \cot^{12}{\left(x \right)} - 1024 \cot^{10}{\left(x \right)} + 1536 \cot^{8}{\left(x \right)} - 1024 \cot^{6}{\left(x \right)} + 256 \cot^{4}{\left(x \right)}} - \frac{2640 \cot^{12}{\left(x \right)} \operatorname{acot}{\left(2 x^{3} \right)}}{256 \cot^{12}{\left(x \right)} - 1024 \cot^{10}{\left(x \right)} + 1536 \cot^{8}{\left(x \right)} - 1024 \cot^{6}{\left(x \right)} + 256 \cot^{4}{\left(x \right)}} + \frac{11232 \cot^{10}{\left(x \right)} \operatorname{acot}{\left(2 x^{3} \right)}}{256 \cot^{12}{\left(x \right)} - 1024 \cot^{10}{\left(x \right)} + 1536 \cot^{8}{\left(x \right)} - 1024 \cot^{6}{\left(x \right)} + 256 \cot^{4}{\left(x \right)}} - \frac{20808 \cot^{8}{\left(x \right)} \operatorname{acot}{\left(2 x^{3} \right)}}{256 \cot^{12}{\left(x \right)} - 1024 \cot^{10}{\left(x \right)} + 1536 \cot^{8}{\left(x \right)} - 1024 \cot^{6}{\left(x \right)} + 256 \cot^{4}{\left(x \right)}} + \frac{11232 \cot^{6}{\left(x \right)} \operatorname{acot}{\left(2 x^{3} \right)}}{256 \cot^{12}{\left(x \right)} - 1024 \cot^{10}{\left(x \right)} + 1536 \cot^{8}{\left(x \right)} - 1024 \cot^{6}{\left(x \right)} + 256 \cot^{4}{\left(x \right)}} - \frac{2640 \cot^{4}{\left(x \right)} \operatorname{acot}{\left(2 x^{3} \right)}}{256 \cot^{12}{\left(x \right)} - 1024 \cot^{10}{\left(x \right)} + 1536 \cot^{8}{\left(x \right)} - 1024 \cot^{6}{\left(x \right)} + 256 \cot^{4}{\left(x \right)}} + \frac{288 \cot^{2}{\left(x \right)} \operatorname{acot}{\left(2 x^{3} \right)}}{256 \cot^{12}{\left(x \right)} - 1024 \cot^{10}{\left(x \right)} + 1536 \cot^{8}{\left(x \right)} - 1024 \cot^{6}{\left(x \right)} + 256 \cot^{4}{\left(x \right)}} - \frac{12 \operatorname{acot}{\left(2 x^{3} \right)}}{256 \cot^{12}{\left(x \right)} - 1024 \cot^{10}{\left(x \right)} + 1536 \cot^{8}{\left(x \right)} - 1024 \cot^{6}{\left(x \right)} + 256 \cot^{4}{\left(x \right)}} - \frac{12 \cot^{8}{\left(x \right)} \operatorname{acot}{\left(2 x^{3} \right)}}{16 \cot^{6}{\left(x \right)} - 32 \cot^{4}{\left(x \right)} + 16 \cot^{2}{\left(x \right)}} + \frac{144 \cot^{6}{\left(x \right)} \operatorname{acot}{\left(2 x^{3} \right)}}{16 \cot^{6}{\left(x \right)} - 32 \cot^{4}{\left(x \right)} + 16 \cot^{2}{\left(x \right)}} - \frac{456 \cot^{4}{\left(x \right)} \operatorname{acot}{\left(2 x^{3} \right)}}{16 \cot^{6}{\left(x \right)} - 32 \cot^{4}{\left(x \right)} + 16 \cot^{2}{\left(x \right)}} + \frac{144 \cot^{2}{\left(x \right)} \operatorname{acot}{\left(2 x^{3} \right)}}{16 \cot^{6}{\left(x \right)} - 32 \cot^{4}{\left(x \right)} + 16 \cot^{2}{\left(x \right)}} - \frac{12 \operatorname{acot}{\left(2 x^{3} \right)}}{16 \cot^{6}{\left(x \right)} - 32 \cot^{4}{\left(x \right)} + 16 \cot^{2}{\left(x \right)}}$$

-12*acot(2*x^3)/(-32*cot(x)^4 + 16*cot(x)^2 + 16*cot(x)^6) - 12*acot(2*x^3)/(-1024*cot(x)^6 - 1024*cot(x)^10 + 256*cot(x)^4 + 256*cot(x)^12 + 1536*cot(x)^8) - 6*x^2/(-192*cot(x)^7 - 64*cot(x)^3 + 64*cot(x)^9 + 192*cot(x)^5 - 768*x^6*cot(x)^7 - 256*x^6*cot(x)^3 + 256*x^6*cot(x)^9 + 768*x^6*cot(x)^5) - 20808*cot(x)^8*acot(2*x^3)/(-1024*cot(x)^6 - 1024*cot(x)^10 + 256*cot(x)^4 + 256*cot(x)^12 + 1536*cot(x)^8) - 2640*cot(x)^4*acot(2*x^3)/(-1024*cot(x)^6 - 1024*cot(x)^10 + 256*cot(x)^4 + 256*cot(x)^12 + 1536*cot(x)^8) - 2640*cot(x)^12*acot(2*x^3)/(-1024*cot(x)^6 - 1024*cot(x)^10 + 256*cot(x)^4 + 256*cot(x)^12 + 1536*cot(x)^8) - 666*x^2*cot(x)^4/(-192*cot(x)^7 - 64*cot(x)^3 + 64*cot(x)^9 + 192*cot(x)^5 - 768*x^6*cot(x)^7 - 256*x^6*cot(x)^3 + 256*x^6*cot(x)^9 + 768*x^6*cot(x)^5) - 666*x^2*cot(x)^8/(-192*cot(x)^7 - 64*cot(x)^3 + 64*cot(x)^9 + 192*cot(x)^5 - 768*x^6*cot(x)^7 - 256*x^6*cot(x)^3 + 256*x^6*cot(x)^9 + 768*x^6*cot(x)^5) - 456*cot(x)^4*acot(2*x^3)/(-32*cot(x)^4 + 16*cot(x)^2 + 16*cot(x)^6) - 12*cot(x)^8*acot(2*x^3)/(-32*cot(x)^4 + 16*cot(x)^2 + 16*cot(x)^6) - 12*cot(x)^16*acot(2*x^3)/(-1024*cot(x)^6 - 1024*cot(x)^10 + 256*cot(x)^4 + 256*cot(x)^12 + 1536*cot(x)^8) - 6*x^2*cot(x)^12/(-192*cot(x)^7 - 64*cot(x)^3 + 64*cot(x)^9 + 192*cot(x)^5 - 768*x^6*cot(x)^7 - 256*x^6*cot(x)^3 + 256*x^6*cot(x)^9 + 768*x^6*cot(x)^5) + 108*x^2*cot(x)^2/(-192*cot(x)^7 - 64*cot(x)^3 + 64*cot(x)^9 + 192*cot(x)^5 - 768*x^6*cot(x)^7 - 256*x^6*cot(x)^3 + 256*x^6*cot(x)^9 + 768*x^6*cot(x)^5) + 108*x^2*cot(x)^10/(-192*cot(x)^7 - 64*cot(x)^3 + 64*cot(x)^9 + 192*cot(x)^5 - 768*x^6*cot(x)^7 - 256*x^6*cot(x)^3 + 256*x^6*cot(x)^9 + 768*x^6*cot(x)^5) + 144*cot(x)^2*acot(2*x^3)/(-32*cot(x)^4 + 16*cot(x)^2 + 16*cot(x)^6) + 144*cot(x)^6*acot(2*x^3)/(-32*cot(x)^4 + 16*cot(x)^2 + 16*cot(x)^6) + 288*cot(x)^2*acot(2*x^3)/(-1024*cot(x)^6 - 1024*cot(x)^10 + 256*cot(x)^4 + 256*cot(x)^12 + 1536*cot(x)^8) + 288*cot(x)^14*acot(2*x^3)/(-1024*cot(x)^6 - 1024*cot(x)^10 + 256*cot(x)^4 + 256*cot(x)^12 + 1536*cot(x)^8) + 1512*x^2*cot(x)^6/(-192*cot(x)^7 - 64*cot(x)^3 + 64*cot(x)^9 + 192*cot(x)^5 - 768*x^6*cot(x)^7 - 256*x^6*cot(x)^3 + 256*x^6*cot(x)^9 + 768*x^6*cot(x)^5) + 11232*cot(x)^6*acot(2*x^3)/(-1024*cot(x)^6 - 1024*cot(x)^10 + 256*cot(x)^4 + 256*cot(x)^12 + 1536*cot(x)^8) + 11232*cot(x)^10*acot(2*x^3)/(-1024*cot(x)^6 - 1024*cot(x)^10 + 256*cot(x)^4 + 256*cot(x)^12 + 1536*cot(x)^8)