Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
log(x^2+1)/2-log(x)+atan(x)/2+(x-2)/(2+2*x^2)
¿Cómo vas a descomponer esta log(x^2+1)/2-log(x)+atan(x)/2+(x-2)/(2+2*x^2) expresión en fracciones?
Solución
Ha introducido
[src]
/ 2 \
log\x + 1/ atan(x) x - 2
----------- - log(x) + ------- + --------
2 2 2
2 + 2*x
$$\frac{x - 2}{2 x^{2} + 2} + \left(\left(- \log{\left(x \right)} + \frac{\log{\left(x^{2} + 1 \right)}}{2}\right) + \frac{\operatorname{atan}{\left(x \right)}}{2}\right)$$
log(x^2 + 1)/2 - log(x) + atan(x)/2 + (x - 2)/(2 + 2*x^2)
Simplificación general
[src]
/ 2\ / / 2\\
-2 + x + \1 + x /*\-2*log(x) + atan(x) + log\1 + x //
-----------------------------------------------------
/ 2\
2*\1 + x /
$$\frac{x + \left(x^{2} + 1\right) \left(- 2 \log{\left(x \right)} + \log{\left(x^{2} + 1 \right)} + \operatorname{atan}{\left(x \right)}\right) - 2}{2 \left(x^{2} + 1\right)}$$
(-2 + x + (1 + x^2)*(-2*log(x) + atan(x) + log(1 + x^2)))/(2*(1 + x^2))
Respuesta numérica
[src]
-log(x) + 0.5*atan(x) + 0.5*log(x^2 + 1) + (-2.0 + x)/(2.0 + 2.0*x^2)
-log(x) + 0.5*atan(x) + 0.5*log(x^2 + 1) + (-2.0 + x)/(2.0 + 2.0*x^2)
Parte trigonométrica
[src]
/ 2\
atan(x) log\1 + x / -2 + x
------- + ----------- - log(x) + --------
2 2 2
2 + 2*x
$$\frac{x - 2}{2 x^{2} + 2} - \log{\left(x \right)} + \frac{\log{\left(x^{2} + 1 \right)}}{2} + \frac{\operatorname{atan}{\left(x \right)}}{2}$$
atan(x)/2 + log(1 + x^2)/2 - log(x) + (-2 + x)/(2 + 2*x^2)
Denominador común
[src]
/ 2\
atan(x) log\1 + x / -2 + x
------- + ----------- - log(x) + --------
2 2 2
2 + 2*x
$$\frac{x - 2}{2 x^{2} + 2} - \log{\left(x \right)} + \frac{\log{\left(x^{2} + 1 \right)}}{2} + \frac{\operatorname{atan}{\left(x \right)}}{2}$$
atan(x)/2 + log(1 + x^2)/2 - log(x) + (-2 + x)/(2 + 2*x^2)
Potencias
[src]
/ 2\
atan(x) log\1 + x / -2 + x
------- + ----------- - log(x) + --------
2 2 2
2 + 2*x
$$\frac{x - 2}{2 x^{2} + 2} - \log{\left(x \right)} + \frac{\log{\left(x^{2} + 1 \right)}}{2} + \frac{\operatorname{atan}{\left(x \right)}}{2}$$
atan(x)/2 + log(1 + x^2)/2 - log(x) + (-2 + x)/(2 + 2*x^2)
Denominador racional
[src]
2 2 / 2\ 2 / 2\
-2 + x - 2*log(x) + x *atan(x) + x *log\1 + x / - 2*x *log(x) + atan(x) + log\1 + x /
-------------------------------------------------------------------------------------
2
2 + 2*x
$$\frac{- 2 x^{2} \log{\left(x \right)} + x^{2} \log{\left(x^{2} + 1 \right)} + x^{2} \operatorname{atan}{\left(x \right)} + x - 2 \log{\left(x \right)} + \log{\left(x^{2} + 1 \right)} + \operatorname{atan}{\left(x \right)} - 2}{2 x^{2} + 2}$$
(-2 + x - 2*log(x) + x^2*atan(x) + x^2*log(1 + x^2) - 2*x^2*log(x) + atan(x) + log(1 + x^2))/(2 + 2*x^2)
Unión de expresiones racionales
[src]
/ 2\ / / 2\\
-2 + x + \1 + x /*\-2*log(x) + atan(x) + log\1 + x //
-----------------------------------------------------
/ 2\
2*\1 + x /
$$\frac{x + \left(x^{2} + 1\right) \left(- 2 \log{\left(x \right)} + \log{\left(x^{2} + 1 \right)} + \operatorname{atan}{\left(x \right)}\right) - 2}{2 \left(x^{2} + 1\right)}$$
(-2 + x + (1 + x^2)*(-2*log(x) + atan(x) + log(1 + x^2)))/(2*(1 + x^2))
Compilar la expresión
[src]
/ 2 \
atan(x) log\x + 1/ -2 + x
------- + ----------- - log(x) + --------
2 2 2
2 + 2*x
$$\frac{x - 2}{2 x^{2} + 2} - \log{\left(x \right)} + \frac{\log{\left(x^{2} + 1 \right)}}{2} + \frac{\operatorname{atan}{\left(x \right)}}{2}$$
atan(x)/2 + log(x^2 + 1)/2 - log(x) + (-2 + x)/(2 + 2*x^2)
Combinatoria
[src]
2 2 / 2\ 2 / 2\
-2 + x - 2*log(x) + x *atan(x) + x *log\1 + x / - 2*x *log(x) + atan(x) + log\1 + x /
-------------------------------------------------------------------------------------
/ 2\
2*\1 + x /
$$\frac{- 2 x^{2} \log{\left(x \right)} + x^{2} \log{\left(x^{2} + 1 \right)} + x^{2} \operatorname{atan}{\left(x \right)} + x - 2 \log{\left(x \right)} + \log{\left(x^{2} + 1 \right)} + \operatorname{atan}{\left(x \right)} - 2}{2 \left(x^{2} + 1\right)}$$
(-2 + x - 2*log(x) + x^2*atan(x) + x^2*log(1 + x^2) - 2*x^2*log(x) + atan(x) + log(1 + x^2))/(2*(1 + x^2))