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

Expresión a simplificar:

Solución

Ha introducido [src]
                  2*atan(2*x + 7)        4*x      
atan(2*x + 7)*2 - --------------- + --------------
                                2                2
                   1 + (2*x + 7)    1 + (2*x + 7) 
4x(2x+7)2+1+(2atan(2x+7)2atan(2x+7)(2x+7)2+1)\frac{4 x}{\left(2 x + 7\right)^{2} + 1} + \left(2 \operatorname{atan}{\left(2 x + 7 \right)} - \frac{2 \operatorname{atan}{\left(2 x + 7 \right)}}{\left(2 x + 7\right)^{2} + 1}\right)
atan(2*x + 7)*2 - 2*atan(2*x + 7)/(1 + (2*x + 7)^2) + (4*x)/(1 + (2*x + 7)^2)
Simplificación general [src]
                            2              
     4*x         2*(7 + 2*x) *atan(7 + 2*x)
-------------- + --------------------------
             2                      2      
1 + (7 + 2*x)          1 + (7 + 2*x)       
4x(2x+7)2+1+2(2x+7)2atan(2x+7)(2x+7)2+1\frac{4 x}{\left(2 x + 7\right)^{2} + 1} + \frac{2 \left(2 x + 7\right)^{2} \operatorname{atan}{\left(2 x + 7 \right)}}{\left(2 x + 7\right)^{2} + 1}
4*x/(1 + (7 + 2*x)^2) + 2*(7 + 2*x)^2*atan(7 + 2*x)/(1 + (7 + 2*x)^2)
Denominador racional [src]
               2              
2*x + (7 + 2*x) *atan(7 + 2*x)
------------------------------
               2              
       25 + 2*x  + 14*x       
2x+(2x+7)2atan(2x+7)2x2+14x+25\frac{2 x + \left(2 x + 7\right)^{2} \operatorname{atan}{\left(2 x + 7 \right)}}{2 x^{2} + 14 x + 25}
(2*x + (7 + 2*x)^2*atan(7 + 2*x))/(25 + 2*x^2 + 14*x)
Respuesta numérica [src]
2.0*atan(2*x + 7) + 4.0*x/(1.0 + 49.0*(1 + 0.285714285714286*x)^2) - 2.0*atan(2*x + 7)/(1.0 + 49.0*(1 + 0.285714285714286*x)^2)
2.0*atan(2*x + 7) + 4.0*x/(1.0 + 49.0*(1 + 0.285714285714286*x)^2) - 2.0*atan(2*x + 7)/(1.0 + 49.0*(1 + 0.285714285714286*x)^2)
Compilar la expresión [src]
                  2*atan(2*x + 7)        4*x      
2*atan(2*x + 7) - --------------- + --------------
                                2                2
                   1 + (7 + 2*x)    1 + (7 + 2*x) 
4x(2x+7)2+1+2atan(2x+7)2atan(2x+7)(2x+7)2+1\frac{4 x}{\left(2 x + 7\right)^{2} + 1} + 2 \operatorname{atan}{\left(2 x + 7 \right)} - \frac{2 \operatorname{atan}{\left(2 x + 7 \right)}}{\left(2 x + 7\right)^{2} + 1}
2*atan(2*x + 7) - 2*atan(2*x + 7)/(1 + (7 + 2*x)^2) + 4*x/(1 + (7 + 2*x)^2)
Parte trigonométrica [src]
                  2*atan(7 + 2*x)        4*x      
2*atan(7 + 2*x) - --------------- + --------------
                                2                2
                   1 + (7 + 2*x)    1 + (7 + 2*x) 
4x(2x+7)2+1+2atan(2x+7)2atan(2x+7)(2x+7)2+1\frac{4 x}{\left(2 x + 7\right)^{2} + 1} + 2 \operatorname{atan}{\left(2 x + 7 \right)} - \frac{2 \operatorname{atan}{\left(2 x + 7 \right)}}{\left(2 x + 7\right)^{2} + 1}
2*atan(7 + 2*x) - 2*atan(7 + 2*x)/(1 + (7 + 2*x)^2) + 4*x/(1 + (7 + 2*x)^2)
Unión de expresiones racionales [src]
  /               2              \
2*\2*x + (7 + 2*x) *atan(7 + 2*x)/
----------------------------------
                       2          
          1 + (7 + 2*x)           
2(2x+(2x+7)2atan(2x+7))(2x+7)2+1\frac{2 \left(2 x + \left(2 x + 7\right)^{2} \operatorname{atan}{\left(2 x + 7 \right)}\right)}{\left(2 x + 7\right)^{2} + 1}
2*(2*x + (7 + 2*x)^2*atan(7 + 2*x))/(1 + (7 + 2*x)^2)
Denominador común [src]
                  -atan(7 + 2*x) + 2*x
2*atan(7 + 2*x) + --------------------
                            2         
                    25 + 2*x  + 14*x  
2xatan(2x+7)2x2+14x+25+2atan(2x+7)\frac{2 x - \operatorname{atan}{\left(2 x + 7 \right)}}{2 x^{2} + 14 x + 25} + 2 \operatorname{atan}{\left(2 x + 7 \right)}
2*atan(7 + 2*x) + (-atan(7 + 2*x) + 2*x)/(25 + 2*x^2 + 14*x)
Combinatoria [src]
                            2                                   
2*x + 49*atan(7 + 2*x) + 4*x *atan(7 + 2*x) + 28*x*atan(7 + 2*x)
----------------------------------------------------------------
                                2                               
                        25 + 2*x  + 14*x                        
4x2atan(2x+7)+28xatan(2x+7)+2x+49atan(2x+7)2x2+14x+25\frac{4 x^{2} \operatorname{atan}{\left(2 x + 7 \right)} + 28 x \operatorname{atan}{\left(2 x + 7 \right)} + 2 x + 49 \operatorname{atan}{\left(2 x + 7 \right)}}{2 x^{2} + 14 x + 25}
(2*x + 49*atan(7 + 2*x) + 4*x^2*atan(7 + 2*x) + 28*x*atan(7 + 2*x))/(25 + 2*x^2 + 14*x)
Potencias [src]
                  2*atan(7 + 2*x)        4*x      
2*atan(7 + 2*x) - --------------- + --------------
                                2                2
                   1 + (7 + 2*x)    1 + (7 + 2*x) 
4x(2x+7)2+1+2atan(2x+7)2atan(2x+7)(2x+7)2+1\frac{4 x}{\left(2 x + 7\right)^{2} + 1} + 2 \operatorname{atan}{\left(2 x + 7 \right)} - \frac{2 \operatorname{atan}{\left(2 x + 7 \right)}}{\left(2 x + 7\right)^{2} + 1}
2*atan(7 + 2*x) - 2*atan(7 + 2*x)/(1 + (7 + 2*x)^2) + 4*x/(1 + (7 + 2*x)^2)