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

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

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