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Simplificación de expresiones/ Descomposición en fracciones simples/ 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)

¿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?

Expresión a simplificar:

Solución

Ha introducido [src] 
                                                  2         3     
    3         2      /            2     \   6*atan (2*x)*cot (4*x)
atan (2*x)*cot (4*x)*\-12 - 12*cot (4*x)/ + ----------------------
                                                          2       
                                                   1 + 4*x
cot⁡2(4x)atan⁡3(2x)(−12cot⁡2(4x)−12)+cot⁡3(4x)6atan⁡2(2x)4x2+1\cot^{2}{\left(4 x \right)} \operatorname{atan}^{3}{\left(2 x \right)} \left(- 12 \cot^{2}{\left(4 x \right)} - 12\right) + \frac{\cot^{3}{\left(4 x \right)} 6 \operatorname{atan}^{2}{\left(2 x \right)}}{4 x^{2} + 1} 
(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)
Simplificación general [src] 
                       /    /       2\                     \
      2         2      |  2*\1 + 4*x /*atan(2*x)           |
6*atan (2*x)*cot (4*x)*|- ---------------------- + cot(4*x)|
                       |           2                       |
                       \        sin (4*x)                  /
------------------------------------------------------------
                                 2                          
                          1 + 4*x
6(−2(4x2+1)atan⁡(2x)sin⁡2(4x)+cot⁡(4x))cot⁡2(4x)atan⁡2(2x)4x2+1\frac{6 \left(- \frac{2 \left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}}{\sin^{2}{\left(4 x \right)}} + \cot{\left(4 x \right)}\right) \cot^{2}{\left(4 x \right)} \operatorname{atan}^{2}{\left(2 x \right)}}{4 x^{2} + 1} 
6*atan(2*x)^2*cot(4*x)^2*(-2*(1 + 4*x^2)*atan(2*x)/sin(4*x)^2 + cot(4*x))/(1 + 4*x^2)
Unión de expresiones racionales [src] 
      2         2      /  /       2\ /        2     \                     \
6*atan (2*x)*cot (4*x)*\2*\1 + 4*x /*\-1 - cot (4*x)/*atan(2*x) + cot(4*x)/
---------------------------------------------------------------------------
                                         2                                 
                                  1 + 4*x
6(2(4x2+1)(−cot⁡2(4x)−1)atan⁡(2x)+cot⁡(4x))cot⁡2(4x)atan⁡2(2x)4x2+1\frac{6 \left(2 \left(4 x^{2} + 1\right) \left(- \cot^{2}{\left(4 x \right)} - 1\right) \operatorname{atan}{\left(2 x \right)} + \cot{\left(4 x \right)}\right) \cot^{2}{\left(4 x \right)} \operatorname{atan}^{2}{\left(2 x \right)}}{4 x^{2} + 1} 
6*atan(2*x)^2*cot(4*x)^2*(2*(1 + 4*x^2)*(-1 - cot(4*x)^2)*atan(2*x) + cot(4*x))/(1 + 4*x^2)
Potencias [src] 
                                                  2         3     
    3         2      /            2     \   6*atan (2*x)*cot (4*x)
atan (2*x)*cot (4*x)*\-12 - 12*cot (4*x)/ + ----------------------
                                                          2       
                                                   1 + 4*x
(−12cot⁡2(4x)−12)cot⁡2(4x)atan⁡3(2x)+6cot⁡3(4x)atan⁡2(2x)4x2+1\left(- 12 \cot^{2}{\left(4 x \right)} - 12\right) \cot^{2}{\left(4 x \right)} \operatorname{atan}^{3}{\left(2 x \right)} + \frac{6 \cot^{3}{\left(4 x \right)} \operatorname{atan}^{2}{\left(2 x \right)}}{4 x^{2} + 1} 
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)
Denominador común [src] 
                                                            2         3     
         3         2               3         4        6*atan (2*x)*cot (4*x)
- 12*atan (2*x)*cot (4*x) - 12*atan (2*x)*cot (4*x) + ----------------------
                                                                    2       
                                                             1 + 4*x
−12cot⁡4(4x)atan⁡3(2x)−12cot⁡2(4x)atan⁡3(2x)+6cot⁡3(4x)atan⁡2(2x)4x2+1- 12 \cot^{4}{\left(4 x \right)} \operatorname{atan}^{3}{\left(2 x \right)} - 12 \cot^{2}{\left(4 x \right)} \operatorname{atan}^{3}{\left(2 x \right)} + \frac{6 \cot^{3}{\left(4 x \right)} \operatorname{atan}^{2}{\left(2 x \right)}}{4 x^{2} + 1} 
-12*atan(2*x)^3*cot(4*x)^2 - 12*atan(2*x)^3*cot(4*x)^4 + 6*atan(2*x)^2*cot(4*x)^3/(1 + 4*x^2)
Denominador racional [src] 
      2         3            3         2      /       2\ /            2     \
6*atan (2*x)*cot (4*x) + atan (2*x)*cot (4*x)*\1 + 4*x /*\-12 - 12*cot (4*x)/
-----------------------------------------------------------------------------
                                          2                                  
                                   1 + 4*x
(4x2+1)(−12cot⁡2(4x)−12)cot⁡2(4x)atan⁡3(2x)+6cot⁡3(4x)atan⁡2(2x)4x2+1\frac{\left(4 x^{2} + 1\right) \left(- 12 \cot^{2}{\left(4 x \right)} - 12\right) \cot^{2}{\left(4 x \right)} \operatorname{atan}^{3}{\left(2 x \right)} + 6 \cot^{3}{\left(4 x \right)} \operatorname{atan}^{2}{\left(2 x \right)}}{4 x^{2} + 1} 
(6*atan(2*x)^2*cot(4*x)^3 + atan(2*x)^3*cot(4*x)^2*(1 + 4*x^2)*(-12 - 12*cot(4*x)^2))/(1 + 4*x^2)
Abrimos la expresión [src] 
                     3                                                          3                                                                                                    2                                                                                                 3         8                                                                 3         4                                                                  3         12                                                                                         2         6                                                                       3         4                                                                        2         2                                                                                                                2         10                                                                      3         8                                                3         16                                                                                        2         12                                                                        3         2                              3         6                                                3         2                                                                 3         14                                                                                          2         4                                                                                                                 2         8                                                                                          3         6                                                                 3         10                            
              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)
6cot⁡12(x)atan⁡2(2x)256x2cot⁡9(x)−768x2cot⁡7(x)+768x2cot⁡5(x)−256x2cot⁡3(x)+64cot⁡9(x)−192cot⁡7(x)+192cot⁡5(x)−64cot⁡3(x)−108cot⁡10(x)atan⁡2(2x)256x2cot⁡9(x)−768x2cot⁡7(x)+768x2cot⁡5(x)−256x2cot⁡3(x)+64cot⁡9(x)−192cot⁡7(x)+192cot⁡5(x)−64cot⁡3(x)+666cot⁡8(x)atan⁡2(2x)256x2cot⁡9(x)−768x2cot⁡7(x)+768x2cot⁡5(x)−256x2cot⁡3(x)+64cot⁡9(x)−192cot⁡7(x)+192cot⁡5(x)−64cot⁡3(x)−1512cot⁡6(x)atan⁡2(2x)256x2cot⁡9(x)−768x2cot⁡7(x)+768x2cot⁡5(x)−256x2cot⁡3(x)+64cot⁡9(x)−192cot⁡7(x)+192cot⁡5(x)−64cot⁡3(x)+666cot⁡4(x)atan⁡2(2x)256x2cot⁡9(x)−768x2cot⁡7(x)+768x2cot⁡5(x)−256x2cot⁡3(x)+64cot⁡9(x)−192cot⁡7(x)+192cot⁡5(x)−64cot⁡3(x)−108cot⁡2(x)atan⁡2(2x)256x2cot⁡9(x)−768x2cot⁡7(x)+768x2cot⁡5(x)−256x2cot⁡3(x)+64cot⁡9(x)−192cot⁡7(x)+192cot⁡5(x)−64cot⁡3(x)+6atan⁡2(2x)256x2cot⁡9(x)−768x2cot⁡7(x)+768x2cot⁡5(x)−256x2cot⁡3(x)+64cot⁡9(x)−192cot⁡7(x)+192cot⁡5(x)−64cot⁡3(x)−12cot⁡16(x)atan⁡3(2x)256cot⁡12(x)−1024cot⁡10(x)+1536cot⁡8(x)−1024cot⁡6(x)+256cot⁡4(x)+288cot⁡14(x)atan⁡3(2x)256cot⁡12(x)−1024cot⁡10(x)+1536cot⁡8(x)−1024cot⁡6(x)+256cot⁡4(x)−2640cot⁡12(x)atan⁡3(2x)256cot⁡12(x)−1024cot⁡10(x)+1536cot⁡8(x)−1024cot⁡6(x)+256cot⁡4(x)+11232cot⁡10(x)atan⁡3(2x)256cot⁡12(x)−1024cot⁡10(x)+1536cot⁡8(x)−1024cot⁡6(x)+256cot⁡4(x)−20808cot⁡8(x)atan⁡3(2x)256cot⁡12(x)−1024cot⁡10(x)+1536cot⁡8(x)−1024cot⁡6(x)+256cot⁡4(x)+11232cot⁡6(x)atan⁡3(2x)256cot⁡12(x)−1024cot⁡10(x)+1536cot⁡8(x)−1024cot⁡6(x)+256cot⁡4(x)−2640cot⁡4(x)atan⁡3(2x)256cot⁡12(x)−1024cot⁡10(x)+1536cot⁡8(x)−1024cot⁡6(x)+256cot⁡4(x)+288cot⁡2(x)atan⁡3(2x)256cot⁡12(x)−1024cot⁡10(x)+1536cot⁡8(x)−1024cot⁡6(x)+256cot⁡4(x)−12atan⁡3(2x)256cot⁡12(x)−1024cot⁡10(x)+1536cot⁡8(x)−1024cot⁡6(x)+256cot⁡4(x)−12cot⁡8(x)atan⁡3(2x)16cot⁡6(x)−32cot⁡4(x)+16cot⁡2(x)+144cot⁡6(x)atan⁡3(2x)16cot⁡6(x)−32cot⁡4(x)+16cot⁡2(x)−456cot⁡4(x)atan⁡3(2x)16cot⁡6(x)−32cot⁡4(x)+16cot⁡2(x)+144cot⁡2(x)atan⁡3(2x)16cot⁡6(x)−32cot⁡4(x)+16cot⁡2(x)−12atan⁡3(2x)16cot⁡6(x)−32cot⁡4(x)+16cot⁡2(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)
Compilar la expresión [src] 
                                                  2         3     
    3         2      /            2     \   6*atan (2*x)*cot (4*x)
atan (2*x)*cot (4*x)*\-12 - 12*cot (4*x)/ + ----------------------
                                                          2       
                                                   1 + 4*x
(−12cot⁡2(4x)−12)cot⁡2(4x)atan⁡3(2x)+6cot⁡3(4x)atan⁡2(2x)4x2+1\left(- 12 \cot^{2}{\left(4 x \right)} - 12\right) \cot^{2}{\left(4 x \right)} \operatorname{atan}^{3}{\left(2 x \right)} + \frac{6 \cot^{3}{\left(4 x \right)} \operatorname{atan}^{2}{\left(2 x \right)}}{4 x^{2} + 1} 
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)
Respuesta numérica [src] 
atan(2*x)^3*cot(4*x)^2*(-12.0 - 12.0*cot(4*x)^2) + 6.0*atan(2*x)^2*cot(4*x)^3/(1.0 + 4.0*x^2)
atan(2*x)^3*cot(4*x)^2*(-12.0 - 12.0*cot(4*x)^2) + 6.0*atan(2*x)^2*cot(4*x)^3/(1.0 + 4.0*x^2)
Combinatoria [src] 
       2         2      /                               2                     2                2    2               \
-6*atan (2*x)*cot (4*x)*\-cot(4*x) + 2*atan(2*x) + 2*cot (4*x)*atan(2*x) + 8*x *atan(2*x) + 8*x *cot (4*x)*atan(2*x)/
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                                                              2                                                      
                                                       1 + 4*x
−6(8x2cot⁡2(4x)atan⁡(2x)+8x2atan⁡(2x)+2cot⁡2(4x)atan⁡(2x)−cot⁡(4x)+2atan⁡(2x))cot⁡2(4x)atan⁡2(2x)4x2+1- \frac{6 \left(8 x^{2} \cot^{2}{\left(4 x \right)} \operatorname{atan}{\left(2 x \right)} + 8 x^{2} \operatorname{atan}{\left(2 x \right)} + 2 \cot^{2}{\left(4 x \right)} \operatorname{atan}{\left(2 x \right)} - \cot{\left(4 x \right)} + 2 \operatorname{atan}{\left(2 x \right)}\right) \cot^{2}{\left(4 x \right)} \operatorname{atan}^{2}{\left(2 x \right)}}{4 x^{2} + 1} 
-6*atan(2*x)^2*cot(4*x)^2*(-cot(4*x) + 2*atan(2*x) + 2*cot(4*x)^2*atan(2*x) + 8*x^2*atan(2*x) + 8*x^2*cot(4*x)^2*atan(2*x))/(1 + 4*x^2)
    © Sr Examen – Калькулятор