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Simplificación de expresiones/ Descomposición en fracciones simples/ log(x^2+1)/2-log(x+1)+atan(x)-1/(1+x)

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

Expresión a simplificar:

Solución

Ha introducido [src] 
   / 2    \                               
log\x  + 1/                            1  
----------- - log(x + 1) + atan(x) - -----
     2                               1 + x
((−log⁡(x+1)+log⁡(x2+1)2)+atan⁡(x))−1x+1\left(\left(- \log{\left(x + 1 \right)} + \frac{\log{\left(x^{2} + 1 \right)}}{2}\right) + \operatorname{atan}{\left(x \right)}\right) - \frac{1}{x + 1} 
log(x^2 + 1)/2 - log(x + 1) + atan(x) - 1/(1 + x)
Simplificación general [src] 
             /                               /     2\\
-2 + (1 + x)*\-2*log(1 + x) + 2*atan(x) + log\1 + x //
------------------------------------------------------
                      2*(1 + x)
(x+1)(−2log⁡(x+1)+log⁡(x2+1)+2atan⁡(x))−22(x+1)\frac{\left(x + 1\right) \left(- 2 \log{\left(x + 1 \right)} + \log{\left(x^{2} + 1 \right)} + 2 \operatorname{atan}{\left(x \right)}\right) - 2}{2 \left(x + 1\right)} 
(-2 + (1 + x)*(-2*log(1 + x) + 2*atan(x) + log(1 + x^2)))/(2*(1 + x))
Parte trigonométrica [src] 
   /     2\                               
log\1 + x /     1                         
----------- - ----- - log(1 + x) + atan(x)
     2        1 + x
−log⁡(x+1)+log⁡(x2+1)2+atan⁡(x)−1x+1- \log{\left(x + 1 \right)} + \frac{\log{\left(x^{2} + 1 \right)}}{2} + \operatorname{atan}{\left(x \right)} - \frac{1}{x + 1} 
log(1 + x^2)/2 - 1/(1 + x) - log(1 + x) + atan(x)
Denominador común [src] 
   /     2\                               
log\1 + x /     1                         
----------- - ----- - log(1 + x) + atan(x)
     2        1 + x
−log⁡(x+1)+log⁡(x2+1)2+atan⁡(x)−1x+1- \log{\left(x + 1 \right)} + \frac{\log{\left(x^{2} + 1 \right)}}{2} + \operatorname{atan}{\left(x \right)} - \frac{1}{x + 1} 
log(1 + x^2)/2 - 1/(1 + x) - log(1 + x) + atan(x)
Respuesta numérica [src] 
-1/(1.0 + x) - log(x + 1) + 0.5*log(x^2 + 1) + atan(x)
-1/(1.0 + x) - log(x + 1) + 0.5*log(x^2 + 1) + atan(x)
Unión de expresiones racionales [src] 
             /                               /     2\\
-2 + (1 + x)*\-2*log(1 + x) + 2*atan(x) + log\1 + x //
------------------------------------------------------
                      2*(1 + x)
(x+1)(−2log⁡(x+1)+log⁡(x2+1)+2atan⁡(x))−22(x+1)\frac{\left(x + 1\right) \left(- 2 \log{\left(x + 1 \right)} + \log{\left(x^{2} + 1 \right)} + 2 \operatorname{atan}{\left(x \right)}\right) - 2}{2 \left(x + 1\right)} 
(-2 + (1 + x)*(-2*log(1 + x) + 2*atan(x) + log(1 + x^2)))/(2*(1 + x))
Combinatoria [src] 
                                     /     2\                                     /     2\
-2 - 2*log(1 + x) + 2*atan(x) + x*log\1 + x / - 2*x*log(1 + x) + 2*x*atan(x) + log\1 + x /
------------------------------------------------------------------------------------------
                                        2*(1 + x)
−2xlog⁡(x+1)+xlog⁡(x2+1)+2xatan⁡(x)−2log⁡(x+1)+log⁡(x2+1)+2atan⁡(x)−22(x+1)\frac{- 2 x \log{\left(x + 1 \right)} + x \log{\left(x^{2} + 1 \right)} + 2 x \operatorname{atan}{\left(x \right)} - 2 \log{\left(x + 1 \right)} + \log{\left(x^{2} + 1 \right)} + 2 \operatorname{atan}{\left(x \right)} - 2}{2 \left(x + 1\right)} 
(-2 - 2*log(1 + x) + 2*atan(x) + x*log(1 + x^2) - 2*x*log(1 + x) + 2*x*atan(x) + log(1 + x^2))/(2*(1 + x))
Potencias [src] 
   /     2\                               
log\1 + x /     1                         
----------- - ----- - log(1 + x) + atan(x)
     2        1 + x
−log⁡(x+1)+log⁡(x2+1)2+atan⁡(x)−1x+1- \log{\left(x + 1 \right)} + \frac{\log{\left(x^{2} + 1 \right)}}{2} + \operatorname{atan}{\left(x \right)} - \frac{1}{x + 1} 
log(1 + x^2)/2 - 1/(1 + x) - log(1 + x) + atan(x)
Denominador racional [src] 
                                     /     2\                                     /     2\
-2 - 2*log(1 + x) + 2*atan(x) + x*log\1 + x / - 2*x*log(1 + x) + 2*x*atan(x) + log\1 + x /
------------------------------------------------------------------------------------------
                                         2 + 2*x
−2xlog⁡(x+1)+xlog⁡(x2+1)+2xatan⁡(x)−2log⁡(x+1)+log⁡(x2+1)+2atan⁡(x)−22x+2\frac{- 2 x \log{\left(x + 1 \right)} + x \log{\left(x^{2} + 1 \right)} + 2 x \operatorname{atan}{\left(x \right)} - 2 \log{\left(x + 1 \right)} + \log{\left(x^{2} + 1 \right)} + 2 \operatorname{atan}{\left(x \right)} - 2}{2 x + 2} 
(-2 - 2*log(1 + x) + 2*atan(x) + x*log(1 + x^2) - 2*x*log(1 + x) + 2*x*atan(x) + log(1 + x^2))/(2 + 2*x)
Compilar la expresión [src] 
   / 2    \                               
log\x  + 1/     1                         
----------- - ----- - log(x + 1) + atan(x)
     2        1 + x
−log⁡(x+1)+log⁡(x2+1)2+atan⁡(x)−1x+1- \log{\left(x + 1 \right)} + \frac{\log{\left(x^{2} + 1 \right)}}{2} + \operatorname{atan}{\left(x \right)} - \frac{1}{x + 1} 
log(x^2 + 1)/2 - 1/(1 + x) - log(x + 1) + atan(x)
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