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¿Cómo vas a descomponer esta atan(2*x+7)*2+4*x/(1+(2*x+7)^2)-(28+8*x)/(2*(1+(2*x+7)^4)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src]
                       4*x              28 + 8*x     
atan(2*x + 7)*2 + -------------- - ------------------
                               2     /             4\
                  1 + (2*x + 7)    2*\1 + (2*x + 7) /
$$- \frac{8 x + 28}{2 \left(\left(2 x + 7\right)^{4} + 1\right)} + \left(\frac{4 x}{\left(2 x + 7\right)^{2} + 1} + 2 \operatorname{atan}{\left(2 x + 7 \right)}\right)$$
atan(2*x + 7)*2 + (4*x)/(1 + (2*x + 7)^2) - (28 + 8*x)/(2*(1 + (2*x + 7)^4))
Simplificación general [src]
                      28 + 8*x            4*x      
2*atan(7 + 2*x) - ---------------- + --------------
                                 4                2
                  2 + 2*(7 + 2*x)    1 + (7 + 2*x) 
$$\frac{4 x}{\left(2 x + 7\right)^{2} + 1} - \frac{8 x + 28}{2 \left(2 x + 7\right)^{4} + 2} + 2 \operatorname{atan}{\left(2 x + 7 \right)}$$
2*atan(7 + 2*x) - (28 + 8*x)/(2 + 2*(7 + 2*x)^4) + 4*x/(1 + (7 + 2*x)^2)
Respuesta numérica [src]
2.0*atan(2*x + 7) - (28.0 + 8.0*x)/(2.0 + 4802.0*(1 + 0.285714285714286*x)^4) + 4.0*x/(1.0 + 49.0*(1 + 0.285714285714286*x)^2)
2.0*atan(2*x + 7) - (28.0 + 8.0*x)/(2.0 + 4802.0*(1 + 0.285714285714286*x)^4) + 4.0*x/(1.0 + 49.0*(1 + 0.285714285714286*x)^2)
Parte trigonométrica [src]
                      28 + 8*x            4*x      
2*atan(7 + 2*x) - ---------------- + --------------
                                 4                2
                  2 + 2*(7 + 2*x)    1 + (7 + 2*x) 
$$\frac{4 x}{\left(2 x + 7\right)^{2} + 1} - \frac{8 x + 28}{2 \left(2 x + 7\right)^{4} + 2} + 2 \operatorname{atan}{\left(2 x + 7 \right)}$$
2*atan(7 + 2*x) - (28 + 8*x)/(2 + 2*(7 + 2*x)^4) + 4*x/(1 + (7 + 2*x)^2)
Potencias [src]
                      28 + 8*x            4*x      
2*atan(7 + 2*x) - ---------------- + --------------
                                 4                2
                  2 + 2*(7 + 2*x)    1 + (7 + 2*x) 
$$\frac{4 x}{\left(2 x + 7\right)^{2} + 1} - \frac{8 x + 28}{2 \left(2 x + 7\right)^{4} + 2} + 2 \operatorname{atan}{\left(2 x + 7 \right)}$$
                     -28 - 8*x            4*x      
2*atan(7 + 2*x) + ---------------- + --------------
                                 4                2
                  2 + 2*(7 + 2*x)    1 + (7 + 2*x) 
$$\frac{4 x}{\left(2 x + 7\right)^{2} + 1} + \frac{- 8 x - 28}{2 \left(2 x + 7\right)^{4} + 2} + 2 \operatorname{atan}{\left(2 x + 7 \right)}$$
2*atan(7 + 2*x) + (-28 - 8*x)/(2 + 2*(7 + 2*x)^4) + 4*x/(1 + (7 + 2*x)^2)
Compilar la expresión [src]
                      28 + 8*x            4*x      
2*atan(2*x + 7) - ---------------- + --------------
                                 4                2
                  2 + 2*(7 + 2*x)    1 + (7 + 2*x) 
$$\frac{4 x}{\left(2 x + 7\right)^{2} + 1} - \frac{8 x + 28}{2 \left(2 x + 7\right)^{4} + 2} + 2 \operatorname{atan}{\left(2 x + 7 \right)}$$
2*atan(2*x + 7) - (28 + 8*x)/(2 + 2*(7 + 2*x)^4) + 4*x/(1 + (7 + 2*x)^2)
Unión de expresiones racionales [src]
  //             4\ /      /             2\              \   /             2\          \
2*\\1 + (7 + 2*x) /*\2*x + \1 + (7 + 2*x) /*atan(7 + 2*x)/ - \1 + (7 + 2*x) /*(7 + 2*x)/
----------------------------------------------------------------------------------------
                           /             2\ /             4\                            
                           \1 + (7 + 2*x) /*\1 + (7 + 2*x) /                            
$$\frac{2 \left(- \left(2 x + 7\right) \left(\left(2 x + 7\right)^{2} + 1\right) + \left(2 x + \left(\left(2 x + 7\right)^{2} + 1\right) \operatorname{atan}{\left(2 x + 7 \right)}\right) \left(\left(2 x + 7\right)^{4} + 1\right)\right)}{\left(\left(2 x + 7\right)^{2} + 1\right) \left(\left(2 x + 7\right)^{4} + 1\right)}$$
2*((1 + (7 + 2*x)^4)*(2*x + (1 + (7 + 2*x)^2)*atan(7 + 2*x)) - (1 + (7 + 2*x)^2)*(7 + 2*x))/((1 + (7 + 2*x)^2)*(1 + (7 + 2*x)^4))
Combinatoria [src]
           5        4         3                  2                             6                      5                       4                        3                        2                                       
-175 + 16*x  + 224*x  + 1172*x  + 2254*x + 2702*x  + 60050*atan(7 + 2*x) + 32*x *atan(7 + 2*x) + 672*x *atan(7 + 2*x) + 5888*x *atan(7 + 2*x) + 27552*x *atan(7 + 2*x) + 72620*x *atan(7 + 2*x) + 102228*x*atan(7 + 2*x)
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                              /        2       \ /          4        3        2         \                                                                               
                                                                              \25 + 2*x  + 14*x/*\1201 + 8*x  + 112*x  + 588*x  + 1372*x/                                                                               
$$\frac{32 x^{6} \operatorname{atan}{\left(2 x + 7 \right)} + 672 x^{5} \operatorname{atan}{\left(2 x + 7 \right)} + 16 x^{5} + 5888 x^{4} \operatorname{atan}{\left(2 x + 7 \right)} + 224 x^{4} + 27552 x^{3} \operatorname{atan}{\left(2 x + 7 \right)} + 1172 x^{3} + 72620 x^{2} \operatorname{atan}{\left(2 x + 7 \right)} + 2702 x^{2} + 102228 x \operatorname{atan}{\left(2 x + 7 \right)} + 2254 x + 60050 \operatorname{atan}{\left(2 x + 7 \right)} - 175}{\left(2 x^{2} + 14 x + 25\right) \left(8 x^{4} + 112 x^{3} + 588 x^{2} + 1372 x + 1201\right)}$$
(-175 + 16*x^5 + 224*x^4 + 1172*x^3 + 2254*x + 2702*x^2 + 60050*atan(7 + 2*x) + 32*x^6*atan(7 + 2*x) + 672*x^5*atan(7 + 2*x) + 5888*x^4*atan(7 + 2*x) + 27552*x^3*atan(7 + 2*x) + 72620*x^2*atan(7 + 2*x) + 102228*x*atan(7 + 2*x))/((25 + 2*x^2 + 14*x)*(1201 + 8*x^4 + 112*x^3 + 588*x^2 + 1372*x))
Denominador común [src]
                                    5        4         3                  2       
                         -175 + 16*x  + 224*x  + 1172*x  + 2254*x + 2702*x        
2*atan(7 + 2*x) + ----------------------------------------------------------------
                              6        5         4          3          2          
                  30025 + 16*x  + 336*x  + 2944*x  + 13776*x  + 36310*x  + 51114*x
$$\frac{16 x^{5} + 224 x^{4} + 1172 x^{3} + 2702 x^{2} + 2254 x - 175}{16 x^{6} + 336 x^{5} + 2944 x^{4} + 13776 x^{3} + 36310 x^{2} + 51114 x + 30025} + 2 \operatorname{atan}{\left(2 x + 7 \right)}$$
2*atan(7 + 2*x) + (-175 + 16*x^5 + 224*x^4 + 1172*x^3 + 2254*x + 2702*x^2)/(30025 + 16*x^6 + 336*x^5 + 2944*x^4 + 13776*x^3 + 36310*x^2 + 51114*x)
Abrimos la expresión [src]
     4*x                                28 + 8*x     
-------------- + atan(2*x + 7)*2 - ------------------
             2                       /             4\
1 + (2*x + 7)                      2*\1 + (2*x + 7) /
$$\frac{4 x}{\left(2 x + 7\right)^{2} + 1} - \frac{8 x + 28}{2 \left(\left(2 x + 7\right)^{4} + 1\right)} + 2 \operatorname{atan}{\left(2 x + 7 \right)}$$
(4*x)/(1 + (2*x + 7)^2) + atan(2*x + 7)*2 - (28 + 8*x)/(2*(1 + (2*x + 7)^4))
Denominador racional [src]
                  2                                  2              2                            4                            6                              4
-28 - 28*(7 + 2*x)  + 4*atan(7 + 2*x) - 8*x*(7 + 2*x)  + 4*(7 + 2*x) *atan(7 + 2*x) + 4*(7 + 2*x) *atan(7 + 2*x) + 4*(7 + 2*x) *atan(7 + 2*x) + 8*x*(7 + 2*x) 
--------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                /        2       \ /           4        3         2         \                                                 
                                                \50 + 4*x  + 28*x/*\4804 + 32*x  + 448*x  + 2352*x  + 5488*x/                                                 
$$\frac{8 x \left(2 x + 7\right)^{4} - 8 x \left(2 x + 7\right)^{2} + 4 \left(2 x + 7\right)^{6} \operatorname{atan}{\left(2 x + 7 \right)} + 4 \left(2 x + 7\right)^{4} \operatorname{atan}{\left(2 x + 7 \right)} + 4 \left(2 x + 7\right)^{2} \operatorname{atan}{\left(2 x + 7 \right)} - 28 \left(2 x + 7\right)^{2} + 4 \operatorname{atan}{\left(2 x + 7 \right)} - 28}{\left(4 x^{2} + 28 x + 50\right) \left(32 x^{4} + 448 x^{3} + 2352 x^{2} + 5488 x + 4804\right)}$$
(-28 - 28*(7 + 2*x)^2 + 4*atan(7 + 2*x) - 8*x*(7 + 2*x)^2 + 4*(7 + 2*x)^2*atan(7 + 2*x) + 4*(7 + 2*x)^4*atan(7 + 2*x) + 4*(7 + 2*x)^6*atan(7 + 2*x) + 8*x*(7 + 2*x)^4)/((50 + 4*x^2 + 28*x)*(4804 + 32*x^4 + 448*x^3 + 2352*x^2 + 5488*x))