Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
pi/(sqrt(1-x^2)*(exp(x)-log(x)))+pi*(1/x-exp(x))*asin(x)/(exp(x)-log(x))^2
¿Cómo vas a descomponer esta pi/(sqrt(1-x^2)*(exp(x)-log(x)))+pi*(1/x-exp(x))*asin(x)/(exp(x)-log(x))^2 expresión en fracciones?
Solución
Ha introducido
[src]
/1 x\
pi*|- - e |*asin(x)
pi \x /
------------------------- + -------------------
________ 2
/ 2 / x \ / x \
\/ 1 - x *\e - log(x)/ \e - log(x)/
$$\frac{\pi \left(- e^{x} + \frac{1}{x}\right) \operatorname{asin}{\left(x \right)}}{\left(e^{x} - \log{\left(x \right)}\right)^{2}} + \frac{\pi}{\sqrt{1 - x^{2}} \left(e^{x} - \log{\left(x \right)}\right)}$$
pi/((sqrt(1 - x^2)*(exp(x) - log(x)))) + ((pi*(1/x - exp(x)))*asin(x))/(exp(x) - log(x))^2
Simplificación general
[src]
/ ________ \
| / x\ / 2 / x\ |
pi*\x*\-log(x) + e / - \/ 1 - x *\-1 + x*e /*asin(x)/
-------------------------------------------------------
________ 2
/ 2 / x\
x*\/ 1 - x *\-log(x) + e /
$$\frac{\pi \left(x \left(e^{x} - \log{\left(x \right)}\right) - \sqrt{1 - x^{2}} \left(x e^{x} - 1\right) \operatorname{asin}{\left(x \right)}\right)}{x \sqrt{1 - x^{2}} \left(e^{x} - \log{\left(x \right)}\right)^{2}}$$
pi*(x*(-log(x) + exp(x)) - sqrt(1 - x^2)*(-1 + x*exp(x))*asin(x))/(x*sqrt(1 - x^2)*(-log(x) + exp(x))^2)
Unión de expresiones racionales
[src]
/ ________ \
| / x\ / 2 / x\ |
pi*\x*\-log(x) + e / + \/ 1 - x *\1 - x*e /*asin(x)/
------------------------------------------------------
________ 2
/ 2 / x\
x*\/ 1 - x *\-log(x) + e /
$$\frac{\pi \left(x \left(e^{x} - \log{\left(x \right)}\right) + \sqrt{1 - x^{2}} \left(- x e^{x} + 1\right) \operatorname{asin}{\left(x \right)}\right)}{x \sqrt{1 - x^{2}} \left(e^{x} - \log{\left(x \right)}\right)^{2}}$$
pi*(x*(-log(x) + exp(x)) + sqrt(1 - x^2)*(1 - x*exp(x))*asin(x))/(x*sqrt(1 - x^2)*(-log(x) + exp(x))^2)
Denominador común
[src]
/ ________ ________ \
| x / 2 / 2 x|
-\pi*x*log(x) - pi*x*e - pi*\/ 1 - x *asin(x) + pi*x*\/ 1 - x *asin(x)*e /
--------------------------------------------------------------------------------
________ ________ ________
/ 2 2 / 2 2*x / 2 x
x*\/ 1 - x *log (x) + x*\/ 1 - x *e - 2*x*\/ 1 - x *e *log(x)
$$- \frac{\pi x \sqrt{1 - x^{2}} e^{x} \operatorname{asin}{\left(x \right)} - \pi x e^{x} + \pi x \log{\left(x \right)} - \pi \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}}{x \sqrt{1 - x^{2}} e^{2 x} - 2 x \sqrt{1 - x^{2}} e^{x} \log{\left(x \right)} + x \sqrt{1 - x^{2}} \log{\left(x \right)}^{2}}$$
-(pi*x*log(x) - pi*x*exp(x) - pi*sqrt(1 - x^2)*asin(x) + pi*x*sqrt(1 - x^2)*asin(x)*exp(x))/(x*sqrt(1 - x^2)*log(x)^2 + x*sqrt(1 - x^2)*exp(2*x) - 2*x*sqrt(1 - x^2)*exp(x)*log(x))
Denominador racional
[src]
________ 2
x 2*x 2 x / 2 / x\ 2 3 2*x 3 x x
pi*asin(x)*log(x) - pi*asin(x)*e + pi*x*asin(x)*e + pi*x *asin(x)*e - pi*x*\/ 1 - x *\-log(x) + e / - pi*x *asin(x)*log(x) - pi*x *asin(x)*e + pi*x *asin(x)*e *log(x) - pi*x*asin(x)*e *log(x)
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3
/ 2\ / x\
x*\-1 + x /*\-log(x) + e /
$$\frac{- \pi x^{3} e^{2 x} \operatorname{asin}{\left(x \right)} + \pi x^{3} e^{x} \log{\left(x \right)} \operatorname{asin}{\left(x \right)} + \pi x^{2} e^{x} \operatorname{asin}{\left(x \right)} - \pi x^{2} \log{\left(x \right)} \operatorname{asin}{\left(x \right)} - \pi x \sqrt{1 - x^{2}} \left(e^{x} - \log{\left(x \right)}\right)^{2} + \pi x e^{2 x} \operatorname{asin}{\left(x \right)} - \pi x e^{x} \log{\left(x \right)} \operatorname{asin}{\left(x \right)} - \pi e^{x} \operatorname{asin}{\left(x \right)} + \pi \log{\left(x \right)} \operatorname{asin}{\left(x \right)}}{x \left(x^{2} - 1\right) \left(e^{x} - \log{\left(x \right)}\right)^{3}}$$
(pi*asin(x)*log(x) - pi*asin(x)*exp(x) + pi*x*asin(x)*exp(2*x) + pi*x^2*asin(x)*exp(x) - pi*x*sqrt(1 - x^2)*(-log(x) + exp(x))^2 - pi*x^2*asin(x)*log(x) - pi*x^3*asin(x)*exp(2*x) + pi*x^3*asin(x)*exp(x)*log(x) - pi*x*asin(x)*exp(x)*log(x))/(x*(-1 + x^2)*(-log(x) + exp(x))^3)
Combinatoria
[src]
/ ________ ________ \
| x / 2 / 2 x|
-pi*\x*log(x) - x*e - \/ 1 - x *asin(x) + x*\/ 1 - x *asin(x)*e /
-----------------------------------------------------------------------
2
___________________ / x\
x*\/ -(1 + x)*(-1 + x) *\-log(x) + e /
$$- \frac{\pi \left(x \sqrt{1 - x^{2}} e^{x} \operatorname{asin}{\left(x \right)} - x e^{x} + x \log{\left(x \right)} - \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}\right)}{x \sqrt{- \left(x - 1\right) \left(x + 1\right)} \left(e^{x} - \log{\left(x \right)}\right)^{2}}$$
-pi*(x*log(x) - x*exp(x) - sqrt(1 - x^2)*asin(x) + x*sqrt(1 - x^2)*asin(x)*exp(x))/(x*sqrt(-(1 + x)*(-1 + x))*(-log(x) + exp(x))^2)
Respuesta numérica
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3.14159265358979*(1.0 - x^2)^(-0.5)/(-log(x) + exp(x)) + (3.14159265358979/x - 3.14159265358979*exp(x))*asin(x)/(-log(x) + exp(x))^2
3.14159265358979*(1.0 - x^2)^(-0.5)/(-log(x) + exp(x)) + (3.14159265358979/x - 3.14159265358979*exp(x))*asin(x)/(-log(x) + exp(x))^2
Parte trigonométrica
[src]
/ 1 \
pi*|- - + cosh(x) + sinh(x)|*asin(x)
pi \ x /
----------------------------------------- - ------------------------------------
________ 2
/ 2 (-log(x) + cosh(x) + sinh(x))
\/ 1 - x *(-log(x) + cosh(x) + sinh(x))
$$- \frac{\pi \left(\sinh{\left(x \right)} + \cosh{\left(x \right)} - \frac{1}{x}\right) \operatorname{asin}{\left(x \right)}}{\left(- \log{\left(x \right)} + \sinh{\left(x \right)} + \cosh{\left(x \right)}\right)^{2}} + \frac{\pi}{\sqrt{1 - x^{2}} \left(- \log{\left(x \right)} + \sinh{\left(x \right)} + \cosh{\left(x \right)}\right)}$$
/1 \
pi*|- - cosh(x) - sinh(x)|*asin(x)
pi \x /
----------------------------------------- + ----------------------------------
________ 2
/ 2 (-log(x) + cosh(x) + sinh(x))
\/ 1 - x *(-log(x) + cosh(x) + sinh(x))
$$\frac{\pi \left(- \sinh{\left(x \right)} - \cosh{\left(x \right)} + \frac{1}{x}\right) \operatorname{asin}{\left(x \right)}}{\left(- \log{\left(x \right)} + \sinh{\left(x \right)} + \cosh{\left(x \right)}\right)^{2}} + \frac{\pi}{\sqrt{1 - x^{2}} \left(- \log{\left(x \right)} + \sinh{\left(x \right)} + \cosh{\left(x \right)}\right)}$$
pi/(sqrt(1 - x^2)*(-log(x) + cosh(x) + sinh(x))) + pi*(1/x - cosh(x) - sinh(x))*asin(x)/(-log(x) + cosh(x) + sinh(x))^2