Sr Examen

Otras calculadoras

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

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

Expresión a simplificar:

Solución

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