Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
tan(E^asin(x))^3/(2*sqrt(x))+3*sqrt(x)*tan(E^asin(x))^2*(1+tan(E^asin(x))^2)*exp(asin(x))/sqrt(1-x^2)
¿Cómo vas a descomponer esta tan(E^asin(x))^3/(2*sqrt(x))+3*sqrt(x)*tan(E^asin(x))^2*(1+tan(E^asin(x))^2)*exp(asin(x))/sqrt(1-x^2) expresión en fracciones?
Solución
Ha introducido
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3/ asin(x)\ ___ 2/ asin(x)\ / 2/ asin(x)\\ asin(x)
tan \E / 3*\/ x *tan \E /*\1 + tan \E //*e
-------------- + ----------------------------------------------------
___ ________
2*\/ x / 2
\/ 1 - x
$$\frac{3 \sqrt{x} \tan^{2}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)} \left(\tan^{2}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)} + 1\right) e^{\operatorname{asin}{\left(x \right)}}}{\sqrt{1 - x^{2}}} + \frac{\tan^{3}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)}}{2 \sqrt{x}}$$
tan(E^asin(x))^3/((2*sqrt(x))) + ((((3*sqrt(x))*tan(E^asin(x))^2)*(1 + tan(E^asin(x))^2))*exp(asin(x)))/sqrt(1 - x^2)
Simplificación general
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3/ asin(x)\ ___ 2/ asin(x)\ asin(x)
tan \e / 3*\/ x *tan \e /*e
-------------- + -------------------------------
___ ________
2*\/ x / 2 2/ asin(x)\
\/ 1 - x *cos \e /
$$\frac{3 \sqrt{x} e^{\operatorname{asin}{\left(x \right)}} \tan^{2}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)}}{\sqrt{1 - x^{2}} \cos^{2}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)}} + \frac{\tan^{3}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)}}{2 \sqrt{x}}$$
tan(exp(asin(x)))^3/(2*sqrt(x)) + 3*sqrt(x)*tan(exp(asin(x)))^2*exp(asin(x))/(sqrt(1 - x^2)*cos(exp(asin(x)))^2)
Respuesta numérica
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0.5*x^(-0.5)*tan(E^asin(x))^3 + 3.0*x^0.5*(1.0 - x^2)^(-0.5)*tan(E^asin(x))^2*(1.0 + tan(E^asin(x))^2)*exp(asin(x))
0.5*x^(-0.5)*tan(E^asin(x))^3 + 3.0*x^0.5*(1.0 - x^2)^(-0.5)*tan(E^asin(x))^2*(1.0 + tan(E^asin(x))^2)*exp(asin(x))
Potencias
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/ 2\
2 | / asin(x) asin(x)\ |
/ asin(x) asin(x)\ | | I*e -I*e | |
___ | I*e -I*e | | \- e + e / | asin(x)
3*\/ x *\- e + e / *|1 - -------------------------------|*e
3 | 2 |
/ asin(x) asin(x)\ | / asin(x) asin(x)\ |
| I*e -I*e | | | I*e -I*e | |
I*\- e + e / \ \e + e / /
- ------------------------------------- - --------------------------------------------------------------------------------------
3 2
/ asin(x) asin(x)\ ________ / asin(x) asin(x)\
___ | I*e -I*e | / 2 | I*e -I*e |
2*\/ x *\e + e / \/ 1 - x *\e + e /
$$- \frac{3 \sqrt{x} \left(- \frac{\left(- e^{i e^{\operatorname{asin}{\left(x \right)}}} + e^{- i e^{\operatorname{asin}{\left(x \right)}}}\right)^{2}}{\left(e^{i e^{\operatorname{asin}{\left(x \right)}}} + e^{- i e^{\operatorname{asin}{\left(x \right)}}}\right)^{2}} + 1\right) \left(- e^{i e^{\operatorname{asin}{\left(x \right)}}} + e^{- i e^{\operatorname{asin}{\left(x \right)}}}\right)^{2} e^{\operatorname{asin}{\left(x \right)}}}{\sqrt{1 - x^{2}} \left(e^{i e^{\operatorname{asin}{\left(x \right)}}} + e^{- i e^{\operatorname{asin}{\left(x \right)}}}\right)^{2}} - \frac{i \left(- e^{i e^{\operatorname{asin}{\left(x \right)}}} + e^{- i e^{\operatorname{asin}{\left(x \right)}}}\right)^{3}}{2 \sqrt{x} \left(e^{i e^{\operatorname{asin}{\left(x \right)}}} + e^{- i e^{\operatorname{asin}{\left(x \right)}}}\right)^{3}}$$
3/ asin(x)\ ___ 2/ asin(x)\ / 2/ asin(x)\\ asin(x)
tan \e / 3*\/ x *tan \e /*\1 + tan \e //*e
-------------- + ----------------------------------------------------
___ ________
2*\/ x / 2
\/ 1 - x
$$\frac{3 \sqrt{x} \left(\tan^{2}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)} + 1\right) e^{\operatorname{asin}{\left(x \right)}} \tan^{2}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)}}{\sqrt{1 - x^{2}}} + \frac{\tan^{3}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)}}{2 \sqrt{x}}$$
3/ asin(x)\ ___ 2/ asin(x)\ / 2/ asin(x)\\ asin(x)
tan \e / \/ x *tan \e /*\3 + 3*tan \e //*e
-------------- + ----------------------------------------------------
___ ________
2*\/ x / 2
\/ 1 - x
$$\frac{\sqrt{x} \left(3 \tan^{2}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)} + 3\right) e^{\operatorname{asin}{\left(x \right)}} \tan^{2}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)}}{\sqrt{1 - x^{2}}} + \frac{\tan^{3}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)}}{2 \sqrt{x}}$$
tan(exp(asin(x)))^3/(2*sqrt(x)) + sqrt(x)*tan(exp(asin(x)))^2*(3 + 3*tan(exp(asin(x)))^2)*exp(asin(x))/sqrt(1 - x^2)
Combinatoria
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/ ________ \
2/ asin(x)\ | / 2 / asin(x)\ asin(x) 2/ asin(x)\ asin(x)|
tan \e /*\\/ 1 - x *tan\e / + 6*x*e + 6*x*tan \e /*e /
---------------------------------------------------------------------------------------
___ ___________________
2*\/ x *\/ -(1 + x)*(-1 + x)
$$\frac{\left(6 x e^{\operatorname{asin}{\left(x \right)}} \tan^{2}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)} + 6 x e^{\operatorname{asin}{\left(x \right)}} + \sqrt{1 - x^{2}} \tan{\left(e^{\operatorname{asin}{\left(x \right)}} \right)}\right) \tan^{2}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)}}{2 \sqrt{x} \sqrt{- \left(x - 1\right) \left(x + 1\right)}}$$
tan(exp(asin(x)))^2*(sqrt(1 - x^2)*tan(exp(asin(x))) + 6*x*exp(asin(x)) + 6*x*tan(exp(asin(x)))^2*exp(asin(x)))/(2*sqrt(x)*sqrt(-(1 + x)*(-1 + x)))
Denominador común
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________
/ 2 3/ asin(x)\ 2/ asin(x)\ asin(x) 4/ asin(x)\ asin(x)
\/ 1 - x *tan \e / + 6*x*tan \e /*e + 6*x*tan \e /*e
--------------------------------------------------------------------------------------
________
___ / 2
2*\/ x *\/ 1 - x
$$\frac{6 x e^{\operatorname{asin}{\left(x \right)}} \tan^{4}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)} + 6 x e^{\operatorname{asin}{\left(x \right)}} \tan^{2}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)} + \sqrt{1 - x^{2}} \tan^{3}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)}}{2 \sqrt{x} \sqrt{1 - x^{2}}}$$
(sqrt(1 - x^2)*tan(exp(asin(x)))^3 + 6*x*tan(exp(asin(x)))^2*exp(asin(x)) + 6*x*tan(exp(asin(x)))^4*exp(asin(x)))/(2*sqrt(x)*sqrt(1 - x^2))
Denominador racional
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________ ________
3/ asin(x)\ 2 3/ asin(x)\ / 2 2/ asin(x)\ asin(x) / 2 4/ asin(x)\ asin(x)
- tan \e / + x *tan \e / - 6*x*\/ 1 - x *tan \e /*e - 6*x*\/ 1 - x *tan \e /*e
------------------------------------------------------------------------------------------------------------------------
___ / 2\
2*\/ x *\-1 + x /
$$\frac{x^{2} \tan^{3}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)} - 6 x \sqrt{1 - x^{2}} e^{\operatorname{asin}{\left(x \right)}} \tan^{4}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)} - 6 x \sqrt{1 - x^{2}} e^{\operatorname{asin}{\left(x \right)}} \tan^{2}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)} - \tan^{3}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)}}{2 \sqrt{x} \left(x^{2} - 1\right)}$$
(-tan(exp(asin(x)))^3 + x^2*tan(exp(asin(x)))^3 - 6*x*sqrt(1 - x^2)*tan(exp(asin(x)))^2*exp(asin(x)) - 6*x*sqrt(1 - x^2)*tan(exp(asin(x)))^4*exp(asin(x)))/(2*sqrt(x)*(-1 + x^2))
Unión de expresiones racionales
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/ ________ \
2/ asin(x)\ | / 2 / asin(x)\ / 2/ asin(x)\\ asin(x)|
tan \e /*\\/ 1 - x *tan\e / + 6*x*\1 + tan \e //*e /
------------------------------------------------------------------------------
________
___ / 2
2*\/ x *\/ 1 - x
$$\frac{\left(6 x \left(\tan^{2}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)} + 1\right) e^{\operatorname{asin}{\left(x \right)}} + \sqrt{1 - x^{2}} \tan{\left(e^{\operatorname{asin}{\left(x \right)}} \right)}\right) \tan^{2}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)}}{2 \sqrt{x} \sqrt{1 - x^{2}}}$$
tan(exp(asin(x)))^2*(sqrt(1 - x^2)*tan(exp(asin(x))) + 6*x*(1 + tan(exp(asin(x)))^2)*exp(asin(x)))/(2*sqrt(x)*sqrt(1 - x^2))
Compilar la expresión
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3/ asin(x)\ ___ 2/ asin(x)\ / 2/ asin(x)\\ asin(x)
tan \e / 3*\/ x *tan \e /*\1 + tan \e //*e
-------------- + ----------------------------------------------------
___ ________
2*\/ x / 2
\/ 1 - x
$$\frac{3 \sqrt{x} \left(\tan^{2}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)} + 1\right) e^{\operatorname{asin}{\left(x \right)}} \tan^{2}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)}}{\sqrt{1 - x^{2}}} + \frac{\tan^{3}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)}}{2 \sqrt{x}}$$
3/ asin(x)\ ___ 2/ asin(x)\ / 2/ asin(x)\\ asin(x)
tan \E / 3*\/ x *tan \E /*\1 + tan \E //*e
-------------- + ----------------------------------------------------
___ ________
2*\/ x / 2
\/ 1 - x
$$\frac{3 \sqrt{x} \left(\tan^{2}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)} + 1\right) e^{\operatorname{asin}{\left(x \right)}} \tan^{2}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)}}{\sqrt{1 - x^{2}}} + \frac{\tan^{3}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)}}{2 \sqrt{x}}$$
tan(E^asin(x))^3/(2*sqrt(x)) + 3*sqrt(x)*tan(E^asin(x))^2*(1 + tan(E^asin(x))^2)*exp(asin(x))/sqrt(1 - x^2)