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

Expresión a simplificar:

Solución

Ha introducido [src]
   / 2    \              
log\x  + 1/   2*x*atan(x)
----------- + -----------
        2         2      
   1 + x         x  + 1  
2xatan(x)x2+1+log(x2+1)x2+1\frac{2 x \operatorname{atan}{\left(x \right)}}{x^{2} + 1} + \frac{\log{\left(x^{2} + 1 \right)}}{x^{2} + 1}
log(x^2 + 1)/(1 + x^2) + ((2*x)*atan(x))/(x^2 + 1)
Simplificación general [src]
                 /     2\
2*x*atan(x) + log\1 + x /
-------------------------
               2         
          1 + x          
2xatan(x)+log(x2+1)x2+1\frac{2 x \operatorname{atan}{\left(x \right)} + \log{\left(x^{2} + 1 \right)}}{x^{2} + 1}
(2*x*atan(x) + log(1 + x^2))/(1 + x^2)
Denominador racional [src]
                 /     2\
2*x*atan(x) + log\1 + x /
-------------------------
               2         
          1 + x          
2xatan(x)+log(x2+1)x2+1\frac{2 x \operatorname{atan}{\left(x \right)} + \log{\left(x^{2} + 1 \right)}}{x^{2} + 1}
(2*x*atan(x) + log(1 + x^2))/(1 + x^2)
Unión de expresiones racionales [src]
                 /     2\
2*x*atan(x) + log\1 + x /
-------------------------
               2         
          1 + x          
2xatan(x)+log(x2+1)x2+1\frac{2 x \operatorname{atan}{\left(x \right)} + \log{\left(x^{2} + 1 \right)}}{x^{2} + 1}
(2*x*atan(x) + log(1 + x^2))/(1 + x^2)
Respuesta numérica [src]
log(x^2 + 1)/(1.0 + x^2) + 2.0*x*atan(x)/(1.0 + x^2)
log(x^2 + 1)/(1.0 + x^2) + 2.0*x*atan(x)/(1.0 + x^2)
Combinatoria [src]
                 /     2\
2*x*atan(x) + log\1 + x /
-------------------------
               2         
          1 + x          
2xatan(x)+log(x2+1)x2+1\frac{2 x \operatorname{atan}{\left(x \right)} + \log{\left(x^{2} + 1 \right)}}{x^{2} + 1}
(2*x*atan(x) + log(1 + x^2))/(1 + x^2)
Denominador común [src]
                 /     2\
2*x*atan(x) + log\1 + x /
-------------------------
               2         
          1 + x          
2xatan(x)+log(x2+1)x2+1\frac{2 x \operatorname{atan}{\left(x \right)} + \log{\left(x^{2} + 1 \right)}}{x^{2} + 1}
(2*x*atan(x) + log(1 + x^2))/(1 + x^2)