Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
atan(x)+x/(1+x^2)-1/(x+1)-atan(x)/(x^2+1)
¿Cómo vas a descomponer esta atan(x)+x/(1+x^2)-1/(x+1)-atan(x)/(x^2+1) expresión en fracciones?
Solución
Ha introducido
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x 1 atan(x)
atan(x) + ------ - ----- - -------
2 x + 1 2
1 + x x + 1
$$\left(\left(\frac{x}{x^{2} + 1} + \operatorname{atan}{\left(x \right)}\right) - \frac{1}{x + 1}\right) - \frac{\operatorname{atan}{\left(x \right)}}{x^{2} + 1}$$
atan(x) + x/(1 + x^2) - 1/(x + 1) - atan(x)/(x^2 + 1)
Simplificación general
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2 3
-1 + x + x *atan(x) + x *atan(x)
--------------------------------
2 3
1 + x + x + x
$$\frac{x^{3} \operatorname{atan}{\left(x \right)} + x^{2} \operatorname{atan}{\left(x \right)} + x - 1}{x^{3} + x^{2} + x + 1}$$
(-1 + x + x^2*atan(x) + x^3*atan(x))/(1 + x + x^2 + x^3)
Respuesta numérica
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-1/(1.0 + x) + x/(1.0 + x^2) - atan(x)/(1.0 + x^2) + atan(x)
-1/(1.0 + x) + x/(1.0 + x^2) - atan(x)/(1.0 + x^2) + atan(x)
Denominador racional
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/ 2\ / 2 / / 2\ \\ / 2\
\1 + x /*\-1 - x + (1 + x)*\x + \1 + x /*atan(x)// - (1 + x)*\1 + x /*atan(x)
------------------------------------------------------------------------------
2
/ 2\
(1 + x)*\1 + x /
$$\frac{- \left(x + 1\right) \left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)} + \left(x^{2} + 1\right) \left(- x^{2} + \left(x + 1\right) \left(x + \left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}\right) - 1\right)}{\left(x + 1\right) \left(x^{2} + 1\right)^{2}}$$
((1 + x^2)*(-1 - x^2 + (1 + x)*(x + (1 + x^2)*atan(x))) - (1 + x)*(1 + x^2)*atan(x))/((1 + x)*(1 + x^2)^2)
Compilar la expresión
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1 x atan(x)
- ----- + ------ - ------- + atan(x)
1 + x 2 2
1 + x 1 + x
$$\frac{x}{x^{2} + 1} + \operatorname{atan}{\left(x \right)} - \frac{\operatorname{atan}{\left(x \right)}}{x^{2} + 1} - \frac{1}{x + 1}$$
-1/(1 + x) + x/(1 + x^2) - atan(x)/(1 + x^2) + atan(x)
Unión de expresiones racionales
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2 / / 2\ \
-1 - x + (1 + x)*\x + \1 + x /*atan(x)/ - (1 + x)*atan(x)
----------------------------------------------------------
/ 2\
(1 + x)*\1 + x /
$$\frac{- x^{2} + \left(x + 1\right) \left(x + \left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}\right) - \left(x + 1\right) \operatorname{atan}{\left(x \right)} - 1}{\left(x + 1\right) \left(x^{2} + 1\right)}$$
(-1 - x^2 + (1 + x)*(x + (1 + x^2)*atan(x)) - (1 + x)*atan(x))/((1 + x)*(1 + x^2))
Combinatoria
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2 3
-1 + x + x *atan(x) + x *atan(x)
--------------------------------
/ 2\
(1 + x)*\1 + x /
$$\frac{x^{3} \operatorname{atan}{\left(x \right)} + x^{2} \operatorname{atan}{\left(x \right)} + x - 1}{\left(x + 1\right) \left(x^{2} + 1\right)}$$
(-1 + x + x^2*atan(x) + x^3*atan(x))/((1 + x)*(1 + x^2))
Potencias
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1 x atan(x)
- ----- + ------ - ------- + atan(x)
1 + x 2 2
1 + x 1 + x
$$\frac{x}{x^{2} + 1} + \operatorname{atan}{\left(x \right)} - \frac{\operatorname{atan}{\left(x \right)}}{x^{2} + 1} - \frac{1}{x + 1}$$
-1/(1 + x) + x/(1 + x^2) - atan(x)/(1 + x^2) + atan(x)
Parte trigonométrica
[src]
1 x atan(x)
- ----- + ------ - ------- + atan(x)
1 + x 2 2
1 + x 1 + x
$$\frac{x}{x^{2} + 1} + \operatorname{atan}{\left(x \right)} - \frac{\operatorname{atan}{\left(x \right)}}{x^{2} + 1} - \frac{1}{x + 1}$$
-1/(1 + x) + x/(1 + x^2) - atan(x)/(1 + x^2) + atan(x)
Denominador común
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1 - x + x*atan(x) + atan(x)
- --------------------------- + atan(x)
2 3
1 + x + x + x
$$\operatorname{atan}{\left(x \right)} - \frac{x \operatorname{atan}{\left(x \right)} - x + \operatorname{atan}{\left(x \right)} + 1}{x^{3} + x^{2} + x + 1}$$
-(1 - x + x*atan(x) + atan(x))/(1 + x + x^2 + x^3) + atan(x)