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Simplificación de expresiones/ Descomposición en fracciones simples/ cot(4*x)^2*(-12-12*cot(4*x)^2)*atan(2*x^3)+6*x^2*cot(4*x)^3/(1+4*x^6)

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

Expresión a simplificar:

Solución

Ha introducido [src] 
                                               2    3     
   2      /            2     \     /   3\   6*x *cot (4*x)
cot (4*x)*\-12 - 12*cot (4*x)/*atan\2*x / + --------------
                                                      6   
                                               1 + 4*x
6x2cot⁡3(4x)4x6+1+(−12cot⁡2(4x)−12)cot⁡2(4x)atan⁡(2x3)\frac{6 x^{2} \cot^{3}{\left(4 x \right)}}{4 x^{6} + 1} + \left(- 12 \cot^{2}{\left(4 x \right)} - 12\right) \cot^{2}{\left(4 x \right)} \operatorname{atan}{\left(2 x^{3} \right)} 
(cot(4*x)^2*(-12 - 12*cot(4*x)^2))*atan(2*x^3) + ((6*x^2)*cot(4*x)^3)/(1 + 4*x^6)
Simplificación general [src] 
            /                /       6\     /   3\\
     2      | 2            2*\1 + 4*x /*atan\2*x /|
6*cot (4*x)*|x *cot(4*x) - -----------------------|
            |                        2            |
            \                     sin (4*x)       /
---------------------------------------------------
                             6                     
                      1 + 4*x
6(x2cot⁡(4x)−2(4x6+1)atan⁡(2x3)sin⁡2(4x))cot⁡2(4x)4x6+1\frac{6 \left(x^{2} \cot{\left(4 x \right)} - \frac{2 \left(4 x^{6} + 1\right) \operatorname{atan}{\left(2 x^{3} \right)}}{\sin^{2}{\left(4 x \right)}}\right) \cot^{2}{\left(4 x \right)}}{4 x^{6} + 1} 
6*cot(4*x)^2*(x^2*cot(4*x) - 2*(1 + 4*x^6)*atan(2*x^3)/sin(4*x)^2)/(1 + 4*x^6)
Respuesta numérica [src] 
cot(4*x)^2*(-12.0 - 12.0*cot(4*x)^2)*atan(2*x^3) + 6.0*x^2*cot(4*x)^3/(1.0 + 4.0*x^6)
cot(4*x)^2*(-12.0 - 12.0*cot(4*x)^2)*atan(2*x^3) + 6.0*x^2*cot(4*x)^3/(1.0 + 4.0*x^6)
Denominador racional [src] 
   2    3           2      /       6\ /            2     \     /   3\
6*x *cot (4*x) + cot (4*x)*\1 + 4*x /*\-12 - 12*cot (4*x)/*atan\2*x /
---------------------------------------------------------------------
                                      6                              
                               1 + 4*x
6x2cot⁡3(4x)+(4x6+1)(−12cot⁡2(4x)−12)cot⁡2(4x)atan⁡(2x3)4x6+1\frac{6 x^{2} \cot^{3}{\left(4 x \right)} + \left(4 x^{6} + 1\right) \left(- 12 \cot^{2}{\left(4 x \right)} - 12\right) \cot^{2}{\left(4 x \right)} \operatorname{atan}{\left(2 x^{3} \right)}}{4 x^{6} + 1} 
(6*x^2*cot(4*x)^3 + cot(4*x)^2*(1 + 4*x^6)*(-12 - 12*cot(4*x)^2)*atan(2*x^3))/(1 + 4*x^6)
Unión de expresiones racionales [src] 
     2      / 2              /       6\ /        2     \     /   3\\
6*cot (4*x)*\x *cot(4*x) + 2*\1 + 4*x /*\-1 - cot (4*x)/*atan\2*x //
--------------------------------------------------------------------
                                     6                              
                              1 + 4*x
6(x2cot⁡(4x)+2(4x6+1)(−cot⁡2(4x)−1)atan⁡(2x3))cot⁡2(4x)4x6+1\frac{6 \left(x^{2} \cot{\left(4 x \right)} + 2 \left(4 x^{6} + 1\right) \left(- \cot^{2}{\left(4 x \right)} - 1\right) \operatorname{atan}{\left(2 x^{3} \right)}\right) \cot^{2}{\left(4 x \right)}}{4 x^{6} + 1} 
6*cot(4*x)^2*(x^2*cot(4*x) + 2*(1 + 4*x^6)*(-1 - cot(4*x)^2)*atan(2*x^3))/(1 + 4*x^6)
Combinatoria [src] 
      2      /      /   3\    2                 2          /   3\      6     /   3\      6    2          /   3\\
-6*cot (4*x)*\2*atan\2*x / - x *cot(4*x) + 2*cot (4*x)*atan\2*x / + 8*x *atan\2*x / + 8*x *cot (4*x)*atan\2*x //
----------------------------------------------------------------------------------------------------------------
                                                           6                                                    
                                                    1 + 4*x
−6(8x6cot⁡2(4x)atan⁡(2x3)+8x6atan⁡(2x3)−x2cot⁡(4x)+2cot⁡2(4x)atan⁡(2x3)+2atan⁡(2x3))cot⁡2(4x)4x6+1- \frac{6 \left(8 x^{6} \cot^{2}{\left(4 x \right)} \operatorname{atan}{\left(2 x^{3} \right)} + 8 x^{6} \operatorname{atan}{\left(2 x^{3} \right)} - x^{2} \cot{\left(4 x \right)} + 2 \cot^{2}{\left(4 x \right)} \operatorname{atan}{\left(2 x^{3} \right)} + 2 \operatorname{atan}{\left(2 x^{3} \right)}\right) \cot^{2}{\left(4 x \right)}}{4 x^{6} + 1} 
-6*cot(4*x)^2*(2*atan(2*x^3) - x^2*cot(4*x) + 2*cot(4*x)^2*atan(2*x^3) + 8*x^6*atan(2*x^3) + 8*x^6*cot(4*x)^2*atan(2*x^3))/(1 + 4*x^6)
Abrimos la expresión [src] 
                     /   3\                                                     /   3\                                                                                                2                                                                                               8        /   3\                                                             4        /   3\                                                              12        /   3\                                                                                       2    6                                                                          4        /   3\                                                                      2    2                                                                                                                     2    10                                                                         8        /   3\                                            16        /   3\                                                                                      2    12                                                                           2        /   3\                          6        /   3\                                            2        /   3\                                                             14        /   3\                                                                                        2    4                                                                                                                      2    8                                                                                             6        /   3\                                                             10        /   3\                         
              12*atan\2*x /                                              12*atan\2*x /                                                                                             6*x                                                                                       20808*cot (x)*atan\2*x /                                                     2640*cot (x)*atan\2*x /                                                      2640*cot  (x)*atan\2*x /                                                                                 1512*x *cot (x)                                                                456*cot (x)*atan\2*x /                                                                 108*x *cot (x)                                                                                                             108*x *cot  (x)                                                                12*cot (x)*atan\2*x /                                      12*cot  (x)*atan\2*x /                                                                                   6*x *cot  (x)                                                                 144*cot (x)*atan\2*x /                   144*cot (x)*atan\2*x /                                     288*cot (x)*atan\2*x /                                                      288*cot  (x)*atan\2*x /                                                                                   666*x *cot (x)                                                                                                              666*x *cot (x)                                                                                 11232*cot (x)*atan\2*x /                                                    11232*cot  (x)*atan\2*x /                         
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          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              4            2            6               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                6              10             4             12              8               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               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)   - 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)
6x2cot⁡12(x)256x6cot⁡9(x)−768x6cot⁡7(x)+768x6cot⁡5(x)−256x6cot⁡3(x)+64cot⁡9(x)−192cot⁡7(x)+192cot⁡5(x)−64cot⁡3(x)−108x2cot⁡10(x)256x6cot⁡9(x)−768x6cot⁡7(x)+768x6cot⁡5(x)−256x6cot⁡3(x)+64cot⁡9(x)−192cot⁡7(x)+192cot⁡5(x)−64cot⁡3(x)+666x2cot⁡8(x)256x6cot⁡9(x)−768x6cot⁡7(x)+768x6cot⁡5(x)−256x6cot⁡3(x)+64cot⁡9(x)−192cot⁡7(x)+192cot⁡5(x)−64cot⁡3(x)−1512x2cot⁡6(x)256x6cot⁡9(x)−768x6cot⁡7(x)+768x6cot⁡5(x)−256x6cot⁡3(x)+64cot⁡9(x)−192cot⁡7(x)+192cot⁡5(x)−64cot⁡3(x)+666x2cot⁡4(x)256x6cot⁡9(x)−768x6cot⁡7(x)+768x6cot⁡5(x)−256x6cot⁡3(x)+64cot⁡9(x)−192cot⁡7(x)+192cot⁡5(x)−64cot⁡3(x)−108x2cot⁡2(x)256x6cot⁡9(x)−768x6cot⁡7(x)+768x6cot⁡5(x)−256x6cot⁡3(x)+64cot⁡9(x)−192cot⁡7(x)+192cot⁡5(x)−64cot⁡3(x)+6x2256x6cot⁡9(x)−768x6cot⁡7(x)+768x6cot⁡5(x)−256x6cot⁡3(x)+64cot⁡9(x)−192cot⁡7(x)+192cot⁡5(x)−64cot⁡3(x)−12cot⁡16(x)atan⁡(2x3)256cot⁡12(x)−1024cot⁡10(x)+1536cot⁡8(x)−1024cot⁡6(x)+256cot⁡4(x)+288cot⁡14(x)atan⁡(2x3)256cot⁡12(x)−1024cot⁡10(x)+1536cot⁡8(x)−1024cot⁡6(x)+256cot⁡4(x)−2640cot⁡12(x)atan⁡(2x3)256cot⁡12(x)−1024cot⁡10(x)+1536cot⁡8(x)−1024cot⁡6(x)+256cot⁡4(x)+11232cot⁡10(x)atan⁡(2x3)256cot⁡12(x)−1024cot⁡10(x)+1536cot⁡8(x)−1024cot⁡6(x)+256cot⁡4(x)−20808cot⁡8(x)atan⁡(2x3)256cot⁡12(x)−1024cot⁡10(x)+1536cot⁡8(x)−1024cot⁡6(x)+256cot⁡4(x)+11232cot⁡6(x)atan⁡(2x3)256cot⁡12(x)−1024cot⁡10(x)+1536cot⁡8(x)−1024cot⁡6(x)+256cot⁡4(x)−2640cot⁡4(x)atan⁡(2x3)256cot⁡12(x)−1024cot⁡10(x)+1536cot⁡8(x)−1024cot⁡6(x)+256cot⁡4(x)+288cot⁡2(x)atan⁡(2x3)256cot⁡12(x)−1024cot⁡10(x)+1536cot⁡8(x)−1024cot⁡6(x)+256cot⁡4(x)−12atan⁡(2x3)256cot⁡12(x)−1024cot⁡10(x)+1536cot⁡8(x)−1024cot⁡6(x)+256cot⁡4(x)−12cot⁡8(x)atan⁡(2x3)16cot⁡6(x)−32cot⁡4(x)+16cot⁡2(x)+144cot⁡6(x)atan⁡(2x3)16cot⁡6(x)−32cot⁡4(x)+16cot⁡2(x)−456cot⁡4(x)atan⁡(2x3)16cot⁡6(x)−32cot⁡4(x)+16cot⁡2(x)+144cot⁡2(x)atan⁡(2x3)16cot⁡6(x)−32cot⁡4(x)+16cot⁡2(x)−12atan⁡(2x3)16cot⁡6(x)−32cot⁡4(x)+16cot⁡2(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{atan}{\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{atan}{\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{atan}{\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{atan}{\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{atan}{\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{atan}{\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{atan}{\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{atan}{\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{atan}{\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{atan}{\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{atan}{\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{atan}{\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{atan}{\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{atan}{\left(2 x^{3} \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*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*atan(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*atan(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*atan(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) - 456*cot(x)^4*atan(2*x^3)/(-32*cot(x)^4 + 16*cot(x)^2 + 16*cot(x)^6) - 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) - 12*cot(x)^8*atan(2*x^3)/(-32*cot(x)^4 + 16*cot(x)^2 + 16*cot(x)^6) - 12*cot(x)^16*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*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) + 144*cot(x)^2*atan(2*x^3)/(-32*cot(x)^4 + 16*cot(x)^2 + 16*cot(x)^6) + 144*cot(x)^6*atan(2*x^3)/(-32*cot(x)^4 + 16*cot(x)^2 + 16*cot(x)^6) + 288*cot(x)^2*atan(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*atan(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) + 11232*cot(x)^6*atan(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*atan(2*x^3)/(-1024*cot(x)^6 - 1024*cot(x)^10 + 256*cot(x)^4 + 256*cot(x)^12 + 1536*cot(x)^8)
Denominador común [src] 
                                                         2    3     
        2          /   3\         4          /   3\   6*x *cot (4*x)
- 12*cot (4*x)*atan\2*x / - 12*cot (4*x)*atan\2*x / + --------------
                                                                6   
                                                         1 + 4*x
6x2cot⁡3(4x)4x6+1−12cot⁡4(4x)atan⁡(2x3)−12cot⁡2(4x)atan⁡(2x3)\frac{6 x^{2} \cot^{3}{\left(4 x \right)}}{4 x^{6} + 1} - 12 \cot^{4}{\left(4 x \right)} \operatorname{atan}{\left(2 x^{3} \right)} - 12 \cot^{2}{\left(4 x \right)} \operatorname{atan}{\left(2 x^{3} \right)} 
-12*cot(4*x)^2*atan(2*x^3) - 12*cot(4*x)^4*atan(2*x^3) + 6*x^2*cot(4*x)^3/(1 + 4*x^6)
    © Sr Examen – Калькулятор