Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
atan(sqrt(x))/(pi+2)+(x+1)/(2*sqrt(x)*(1+x)*(pi+2))
¿Cómo vas a descomponer esta atan(sqrt(x))/(pi+2)+(x+1)/(2*sqrt(x)*(1+x)*(pi+2)) expresión en fracciones?
Solución
Ha introducido
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/ ___\
atan\\/ x / x + 1
----------- + ------------------------
pi + 2 ___
2*\/ x *(1 + x)*(pi + 2)
$$\frac{\operatorname{atan}{\left(\sqrt{x} \right)}}{2 + \pi} + \frac{x + 1}{2 \sqrt{x} \left(x + 1\right) \left(2 + \pi\right)}$$
atan(sqrt(x))/(pi + 2) + (x + 1)/((((2*sqrt(x))*(1 + x))*(pi + 2)))
Simplificación general
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1 ___ / ___\
- + \/ x *atan\\/ x /
2
---------------------
___
\/ x *(2 + pi)
$$\frac{\sqrt{x} \operatorname{atan}{\left(\sqrt{x} \right)} + \frac{1}{2}}{\sqrt{x} \left(2 + \pi\right)}$$
(1/2 + sqrt(x)*atan(sqrt(x)))/(sqrt(x)*(2 + pi))
Respuesta numérica
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0.0972461324120857*x^(-0.5) + 0.194492264824171*atan(sqrt(x))
0.0972461324120857*x^(-0.5) + 0.194492264824171*atan(sqrt(x))
Combinatoria
[src]
___ / ___\
1 + 2*\/ x *atan\\/ x /
-----------------------
___
2*\/ x *(2 + pi)
$$\frac{2 \sqrt{x} \operatorname{atan}{\left(\sqrt{x} \right)} + 1}{2 \sqrt{x} \left(2 + \pi\right)}$$
(1 + 2*sqrt(x)*atan(sqrt(x)))/(2*sqrt(x)*(2 + pi))
Denominador común
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___ / ___\
1 + 2*\/ x *atan\\/ x /
-----------------------
___ ___
4*\/ x + 2*pi*\/ x
$$\frac{2 \sqrt{x} \operatorname{atan}{\left(\sqrt{x} \right)} + 1}{4 \sqrt{x} + 2 \pi \sqrt{x}}$$
(1 + 2*sqrt(x)*atan(sqrt(x)))/(4*sqrt(x) + 2*pi*sqrt(x))
Compilar la expresión
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/ ___\
atan\\/ x / 1
----------- + ----------------
2 + pi ___
2*\/ x *(2 + pi)
$$\frac{\operatorname{atan}{\left(\sqrt{x} \right)}}{2 + \pi} + \frac{1}{2 \sqrt{x} \left(2 + \pi\right)}$$
atan(sqrt(x))/(2 + pi) + 1/(2*sqrt(x)*(2 + pi))
Denominador racional
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___ 3/2 ___ 3/2 / ___\ 2 / ___\ / ___\ 2 / ___\
2*\/ x + 2*x + pi*\/ x + pi*x + 4*x*atan\\/ x / + 4*x *atan\\/ x / + 2*pi*x*atan\\/ x / + 2*pi*x *atan\\/ x /
---------------------------------------------------------------------------------------------------------------------
2
2*x*(1 + x)*(2 + pi)
$$\frac{2 x^{\frac{3}{2}} + \pi x^{\frac{3}{2}} + 2 \sqrt{x} + \pi \sqrt{x} + 4 x^{2} \operatorname{atan}{\left(\sqrt{x} \right)} + 2 \pi x^{2} \operatorname{atan}{\left(\sqrt{x} \right)} + 4 x \operatorname{atan}{\left(\sqrt{x} \right)} + 2 \pi x \operatorname{atan}{\left(\sqrt{x} \right)}}{2 x \left(2 + \pi\right)^{2} \left(x + 1\right)}$$
(2*sqrt(x) + 2*x^(3/2) + pi*sqrt(x) + pi*x^(3/2) + 4*x*atan(sqrt(x)) + 4*x^2*atan(sqrt(x)) + 2*pi*x*atan(sqrt(x)) + 2*pi*x^2*atan(sqrt(x)))/(2*x*(1 + x)*(2 + pi)^2)
Parte trigonométrica
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/ ___\
atan\\/ x / 1
----------- + ----------------
2 + pi ___
2*\/ x *(2 + pi)
$$\frac{\operatorname{atan}{\left(\sqrt{x} \right)}}{2 + \pi} + \frac{1}{2 \sqrt{x} \left(2 + \pi\right)}$$
atan(sqrt(x))/(2 + pi) + 1/(2*sqrt(x)*(2 + pi))
Potencias
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/ ___\
atan\\/ x / 1
----------- + ----------------
2 + pi ___
2*\/ x *(2 + pi)
$$\frac{\operatorname{atan}{\left(\sqrt{x} \right)}}{2 + \pi} + \frac{1}{2 \sqrt{x} \left(2 + \pi\right)}$$
/ ___\
atan\\/ x / 1 + x
----------- + ------------------------
2 + pi ___
\/ x *(2 + pi)*(2 + 2*x)
$$\frac{\operatorname{atan}{\left(\sqrt{x} \right)}}{2 + \pi} + \frac{x + 1}{\sqrt{x} \left(2 + \pi\right) \left(2 x + 2\right)}$$
atan(sqrt(x))/(2 + pi) + (1 + x)/(sqrt(x)*(2 + pi)*(2 + 2*x))
Unión de expresiones racionales
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___ / ___\
1 + 2*\/ x *atan\\/ x /
-----------------------
___
2*\/ x *(2 + pi)
$$\frac{2 \sqrt{x} \operatorname{atan}{\left(\sqrt{x} \right)} + 1}{2 \sqrt{x} \left(2 + \pi\right)}$$
(1 + 2*sqrt(x)*atan(sqrt(x)))/(2*sqrt(x)*(2 + pi))