Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
acot(x)/(2*x)-log(x)/(2*(1+x^2))
¿Cómo vas a descomponer esta acot(x)/(2*x)-log(x)/(2*(1+x^2)) expresión en fracciones?
Solución
Ha introducido
[src]
acot(x) log(x)
------- - ----------
2*x / 2\
2*\1 + x /
$$- \frac{\log{\left(x \right)}}{2 \left(x^{2} + 1\right)} + \frac{\operatorname{acot}{\left(x \right)}}{2 x}$$
acot(x)/((2*x)) - log(x)/(2*(1 + x^2))
Simplificación general
[src]
/ 2\
\1 + x /*acot(x) - x*log(x)
---------------------------
/ 2\
2*x*\1 + x /
$$\frac{- x \log{\left(x \right)} + \left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}}{2 x \left(x^{2} + 1\right)}$$
((1 + x^2)*acot(x) - x*log(x))/(2*x*(1 + x^2))
Respuesta numérica
[src]
-log(x)/(2.0 + 2.0*x^2) + 0.5*acot(x)/x
-log(x)/(2.0 + 2.0*x^2) + 0.5*acot(x)/x
Parte trigonométrica
[src]
acot(x) log(x)
------- - --------
2*x 2
2 + 2*x
$$- \frac{\log{\left(x \right)}}{2 x^{2} + 2} + \frac{\operatorname{acot}{\left(x \right)}}{2 x}$$
acot(x)/(2*x) - log(x)/(2 + 2*x^2)
Unión de expresiones racionales
[src]
/ 2\
\1 + x /*acot(x) - x*log(x)
---------------------------
/ 2\
2*x*\1 + x /
$$\frac{- x \log{\left(x \right)} + \left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}}{2 x \left(x^{2} + 1\right)}$$
((1 + x^2)*acot(x) - x*log(x))/(2*x*(1 + x^2))
Denominador común
[src]
2
x *acot(x) - x*log(x) + acot(x)
-------------------------------
3
2*x + 2*x
$$\frac{x^{2} \operatorname{acot}{\left(x \right)} - x \log{\left(x \right)} + \operatorname{acot}{\left(x \right)}}{2 x^{3} + 2 x}$$
(x^2*acot(x) - x*log(x) + acot(x))/(2*x + 2*x^3)
Potencias
[src]
acot(x) log(x)
------- - --------
2*x 2
2 + 2*x
$$- \frac{\log{\left(x \right)}}{2 x^{2} + 2} + \frac{\operatorname{acot}{\left(x \right)}}{2 x}$$
acot(x)/(2*x) - log(x)/(2 + 2*x^2)
Combinatoria
[src]
2
x *acot(x) - x*log(x) + acot(x)
-------------------------------
/ 2\
2*x*\1 + x /
$$\frac{x^{2} \operatorname{acot}{\left(x \right)} - x \log{\left(x \right)} + \operatorname{acot}{\left(x \right)}}{2 x \left(x^{2} + 1\right)}$$
(x^2*acot(x) - x*log(x) + acot(x))/(2*x*(1 + x^2))
Denominador racional
[src]
/ 2\
\2 + 2*x /*acot(x) - 2*x*log(x)
-------------------------------
/ 2\
2*x*\2 + 2*x /
$$\frac{- 2 x \log{\left(x \right)} + \left(2 x^{2} + 2\right) \operatorname{acot}{\left(x \right)}}{2 x \left(2 x^{2} + 2\right)}$$
((2 + 2*x^2)*acot(x) - 2*x*log(x))/(2*x*(2 + 2*x^2))
Compilar la expresión
[src]
acot(x) log(x)
------- - --------
2*x 2
2 + 2*x
$$- \frac{\log{\left(x \right)}}{2 x^{2} + 2} + \frac{\operatorname{acot}{\left(x \right)}}{2 x}$$
acot(x)/(2*x) - log(x)/(2 + 2*x^2)