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¿Cómo vas a descomponer esta atan(6*x^3+1)^2+36*x^3*atan(6*x^3+1)/(1+(6*x^3+1)^2) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src]
                      3     /   3    \
    2/   3    \   36*x *atan\6*x  + 1/
atan \6*x  + 1/ + --------------------
                                  2   
                        /   3    \    
                    1 + \6*x  + 1/    
36x3atan(6x3+1)(6x3+1)2+1+atan2(6x3+1)\frac{36 x^{3} \operatorname{atan}{\left(6 x^{3} + 1 \right)}}{\left(6 x^{3} + 1\right)^{2} + 1} + \operatorname{atan}^{2}{\left(6 x^{3} + 1 \right)}
atan(6*x^3 + 1)^2 + ((36*x^3)*atan(6*x^3 + 1))/(1 + (6*x^3 + 1)^2)
Simplificación general [src]
/        /              2\               \               
|    3   |    /       3\ |     /       3\|     /       3\
\36*x  + \1 + \1 + 6*x / /*atan\1 + 6*x //*atan\1 + 6*x /
---------------------------------------------------------
                                   2                     
                         /       3\                      
                     1 + \1 + 6*x /                      
(36x3+((6x3+1)2+1)atan(6x3+1))atan(6x3+1)(6x3+1)2+1\frac{\left(36 x^{3} + \left(\left(6 x^{3} + 1\right)^{2} + 1\right) \operatorname{atan}{\left(6 x^{3} + 1 \right)}\right) \operatorname{atan}{\left(6 x^{3} + 1 \right)}}{\left(6 x^{3} + 1\right)^{2} + 1}
(36*x^3 + (1 + (1 + 6*x^3)^2)*atan(1 + 6*x^3))*atan(1 + 6*x^3)/(1 + (1 + 6*x^3)^2)
Respuesta numérica [src]
atan(6*x^3 + 1)^2 + 36.0*x^3*atan(6*x^3 + 1)/(1.0 + 36.0*(0.166666666666667 + x^3)^2)
atan(6*x^3 + 1)^2 + 36.0*x^3*atan(6*x^3 + 1)/(1.0 + 36.0*(0.166666666666667 + x^3)^2)
Denominador racional [src]
/                  2                                \               
|    3   /       3\      /       3\       /       3\|     /       3\
\36*x  + \1 + 6*x / *atan\1 + 6*x / + atan\1 + 6*x //*atan\1 + 6*x /
--------------------------------------------------------------------
                                 3       6                          
                         2 + 12*x  + 36*x                           
(36x3+(6x3+1)2atan(6x3+1)+atan(6x3+1))atan(6x3+1)36x6+12x3+2\frac{\left(36 x^{3} + \left(6 x^{3} + 1\right)^{2} \operatorname{atan}{\left(6 x^{3} + 1 \right)} + \operatorname{atan}{\left(6 x^{3} + 1 \right)}\right) \operatorname{atan}{\left(6 x^{3} + 1 \right)}}{36 x^{6} + 12 x^{3} + 2}
(36*x^3 + (1 + 6*x^3)^2*atan(1 + 6*x^3) + atan(1 + 6*x^3))*atan(1 + 6*x^3)/(2 + 12*x^3 + 36*x^6)
Unión de expresiones racionales [src]
/        /              2\               \               
|    3   |    /       3\ |     /       3\|     /       3\
\36*x  + \1 + \1 + 6*x / /*atan\1 + 6*x //*atan\1 + 6*x /
---------------------------------------------------------
                                   2                     
                         /       3\                      
                     1 + \1 + 6*x /                      
(36x3+((6x3+1)2+1)atan(6x3+1))atan(6x3+1)(6x3+1)2+1\frac{\left(36 x^{3} + \left(\left(6 x^{3} + 1\right)^{2} + 1\right) \operatorname{atan}{\left(6 x^{3} + 1 \right)}\right) \operatorname{atan}{\left(6 x^{3} + 1 \right)}}{\left(6 x^{3} + 1\right)^{2} + 1}
(36*x^3 + (1 + (1 + 6*x^3)^2)*atan(1 + 6*x^3))*atan(1 + 6*x^3)/(1 + (1 + 6*x^3)^2)
Denominador común [src]
                      3     /       3\
    2/       3\   18*x *atan\1 + 6*x /
atan \1 + 6*x / + --------------------
                           3       6  
                    1 + 6*x  + 18*x   
18x3atan(6x3+1)18x6+6x3+1+atan2(6x3+1)\frac{18 x^{3} \operatorname{atan}{\left(6 x^{3} + 1 \right)}}{18 x^{6} + 6 x^{3} + 1} + \operatorname{atan}^{2}{\left(6 x^{3} + 1 \right)}
atan(1 + 6*x^3)^2 + 18*x^3*atan(1 + 6*x^3)/(1 + 6*x^3 + 18*x^6)
Combinatoria [src]
/    3      3     /       3\       6     /       3\       /       3\\     /       3\
\18*x  + 6*x *atan\1 + 6*x / + 18*x *atan\1 + 6*x / + atan\1 + 6*x //*atan\1 + 6*x /
------------------------------------------------------------------------------------
                                         3       6                                  
                                  1 + 6*x  + 18*x                                   
(18x6atan(6x3+1)+6x3atan(6x3+1)+18x3+atan(6x3+1))atan(6x3+1)18x6+6x3+1\frac{\left(18 x^{6} \operatorname{atan}{\left(6 x^{3} + 1 \right)} + 6 x^{3} \operatorname{atan}{\left(6 x^{3} + 1 \right)} + 18 x^{3} + \operatorname{atan}{\left(6 x^{3} + 1 \right)}\right) \operatorname{atan}{\left(6 x^{3} + 1 \right)}}{18 x^{6} + 6 x^{3} + 1}
(18*x^3 + 6*x^3*atan(1 + 6*x^3) + 18*x^6*atan(1 + 6*x^3) + atan(1 + 6*x^3))*atan(1 + 6*x^3)/(1 + 6*x^3 + 18*x^6)