Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
log(x+e)^acos(x)*(-log(log(x+e))/sqrt(1-x^2)+acos(x)/((x+e)*log(x+e)))
¿Cómo vas a descomponer esta log(x+e)^acos(x)*(-log(log(x+e))/sqrt(1-x^2)+acos(x)/((x+e)*log(x+e))) expresión en fracciones?
Solución
Ha introducido
[src]
acos(x) /-log(log(x + E)) acos(x) \
log (x + E)*|----------------- + ------------------|
| ________ (x + E)*log(x + E)|
| / 2 |
\ \/ 1 - x /
$$\left(\frac{\left(-1\right) \log{\left(\log{\left(x + e \right)} \right)}}{\sqrt{1 - x^{2}}} + \frac{\operatorname{acos}{\left(x \right)}}{\left(x + e\right) \log{\left(x + e \right)}}\right) \log{\left(x + e \right)}^{\operatorname{acos}{\left(x \right)}}$$
log(x + E)^acos(x)*((-log(log(x + E)))/sqrt(1 - x^2) + acos(x)/(((x + E)*log(x + E))))
Simplificación general
[src]
/ ________ \
-1 + acos(x) | / 2 |
log (E + x)*\\/ 1 - x *acos(x) - (E + x)*log(E + x)*log(log(E + x))/
---------------------------------------------------------------------------------
________
/ 2
\/ 1 - x *(E + x)
$$\frac{\left(\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)} - \left(x + e\right) \log{\left(x + e \right)} \log{\left(\log{\left(x + e \right)} \right)}\right) \log{\left(x + e \right)}^{\operatorname{acos}{\left(x \right)} - 1}}{\sqrt{1 - x^{2}} \left(x + e\right)}$$
log(E + x)^(-1 + acos(x))*(sqrt(1 - x^2)*acos(x) - (E + x)*log(E + x)*log(log(E + x)))/(sqrt(1 - x^2)*(E + x))
Respuesta numérica
[src]
log(x + E)^acos(x)*(-(1.0 - x^2)^(-0.5)*log(log(x + E)) + acos(x)/((2.71828182845905 + x)*log(x + E)))
log(x + E)^acos(x)*(-(1.0 - x^2)^(-0.5)*log(log(x + E)) + acos(x)/((2.71828182845905 + x)*log(x + E)))
Denominador racional
[src]
________ ________
-1 + acos(x) 2 -1 + acos(x) / 2 -1 + acos(x) / 2 -1 + acos(x)
- log (E + x)*acos(x) + x *log (E + x)*acos(x) + E*\/ 1 - x *log (E + x)*log(E + x)*log(log(E + x)) + x*\/ 1 - x *log (E + x)*log(E + x)*log(log(E + x))
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ 2\
\-1 + x /*(E + x)
$$\frac{x^{2} \log{\left(x + e \right)}^{\operatorname{acos}{\left(x \right)} - 1} \operatorname{acos}{\left(x \right)} + x \sqrt{1 - x^{2}} \log{\left(x + e \right)} \log{\left(x + e \right)}^{\operatorname{acos}{\left(x \right)} - 1} \log{\left(\log{\left(x + e \right)} \right)} + e \sqrt{1 - x^{2}} \log{\left(x + e \right)} \log{\left(x + e \right)}^{\operatorname{acos}{\left(x \right)} - 1} \log{\left(\log{\left(x + e \right)} \right)} - \log{\left(x + e \right)}^{\operatorname{acos}{\left(x \right)} - 1} \operatorname{acos}{\left(x \right)}}{\left(x + e\right) \left(x^{2} - 1\right)}$$
(-log(E + x)^(-1 + acos(x))*acos(x) + x^2*log(E + x)^(-1 + acos(x))*acos(x) + E*sqrt(1 - x^2)*log(E + x)^(-1 + acos(x))*log(E + x)*log(log(E + x)) + x*sqrt(1 - x^2)*log(E + x)^(-1 + acos(x))*log(E + x)*log(log(E + x)))/((-1 + x^2)*(E + x))
Denominador común
[src]
/ ________ \
| / 2 acos(x) acos(x) acos(x) |
-\- \/ 1 - x *log (E + x)*acos(x) + E*log (E + x)*log(E + x)*log(log(E + x)) + x*log (E + x)*log(E + x)*log(log(E + x))/
---------------------------------------------------------------------------------------------------------------------------------------------
________ ________
/ 2 / 2
E*\/ 1 - x *log(E + x) + x*\/ 1 - x *log(E + x)
$$- \frac{x \log{\left(x + e \right)} \log{\left(x + e \right)}^{\operatorname{acos}{\left(x \right)}} \log{\left(\log{\left(x + e \right)} \right)} - \sqrt{1 - x^{2}} \log{\left(x + e \right)}^{\operatorname{acos}{\left(x \right)}} \operatorname{acos}{\left(x \right)} + e \log{\left(x + e \right)} \log{\left(x + e \right)}^{\operatorname{acos}{\left(x \right)}} \log{\left(\log{\left(x + e \right)} \right)}}{x \sqrt{1 - x^{2}} \log{\left(x + e \right)} + e \sqrt{1 - x^{2}} \log{\left(x + e \right)}}$$
-(-sqrt(1 - x^2)*log(E + x)^acos(x)*acos(x) + E*log(E + x)^acos(x)*log(E + x)*log(log(E + x)) + x*log(E + x)^acos(x)*log(E + x)*log(log(E + x)))/(E*sqrt(1 - x^2)*log(E + x) + x*sqrt(1 - x^2)*log(E + x))
Unión de expresiones racionales
[src]
/ ________ \
acos(x) | / 2 |
log (E + x)*\\/ 1 - x *acos(x) - (E + x)*log(E + x)*log(log(E + x))/
----------------------------------------------------------------------------
________
/ 2
\/ 1 - x *(E + x)*log(E + x)
$$\frac{\left(\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)} - \left(x + e\right) \log{\left(x + e \right)} \log{\left(\log{\left(x + e \right)} \right)}\right) \log{\left(x + e \right)}^{\operatorname{acos}{\left(x \right)}}}{\sqrt{1 - x^{2}} \left(x + e\right) \log{\left(x + e \right)}}$$
log(E + x)^acos(x)*(sqrt(1 - x^2)*acos(x) - (E + x)*log(E + x)*log(log(E + x)))/(sqrt(1 - x^2)*(E + x)*log(E + x))
Combinatoria
[src]
/ ________ \
acos(x) | / 2 |
-log (E + x)*\- \/ 1 - x *acos(x) + E*log(E + x)*log(log(E + x)) + x*log(E + x)*log(log(E + x))/
---------------------------------------------------------------------------------------------------------
___________________
\/ -(1 + x)*(-1 + x) *(E + x)*log(E + x)
$$- \frac{\left(x \log{\left(x + e \right)} \log{\left(\log{\left(x + e \right)} \right)} - \sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)} + e \log{\left(x + e \right)} \log{\left(\log{\left(x + e \right)} \right)}\right) \log{\left(x + e \right)}^{\operatorname{acos}{\left(x \right)}}}{\sqrt{- \left(x - 1\right) \left(x + 1\right)} \left(x + e\right) \log{\left(x + e \right)}}$$
-log(E + x)^acos(x)*(-sqrt(1 - x^2)*acos(x) + E*log(E + x)*log(log(E + x)) + x*log(E + x)*log(log(E + x)))/(sqrt(-(1 + x)*(-1 + x))*(E + x)*log(E + x))
Potencias
[src]
acos(x) / log(log(E + x)) acos(x) \
log (E + x)*|- --------------- + ------------------|
| ________ (E + x)*log(E + x)|
| / 2 |
\ \/ 1 - x /
$$\left(\frac{\operatorname{acos}{\left(x \right)}}{\left(x + e\right) \log{\left(x + e \right)}} - \frac{\log{\left(\log{\left(x + e \right)} \right)}}{\sqrt{1 - x^{2}}}\right) \log{\left(x + e \right)}^{\operatorname{acos}{\left(x \right)}}$$
log(E + x)^acos(x)*(-log(log(E + x))/sqrt(1 - x^2) + acos(x)/((E + x)*log(E + x)))
Compilar la expresión
[src]
acos(x) / log(log(x + E)) acos(x) \
log (x + E)*|- --------------- + ------------------|
| ________ (E + x)*log(x + E)|
| / 2 |
\ \/ 1 - x /
$$\left(\frac{\operatorname{acos}{\left(x \right)}}{\left(x + e\right) \log{\left(x + e \right)}} - \frac{\log{\left(\log{\left(x + e \right)} \right)}}{\sqrt{1 - x^{2}}}\right) \log{\left(x + e \right)}^{\operatorname{acos}{\left(x \right)}}$$
acos(x) / log(log(E + x)) acos(x) \
log (E + x)*|- --------------- + ------------------|
| ________ (E + x)*log(E + x)|
| / 2 |
\ \/ 1 - x /
$$\left(\frac{\operatorname{acos}{\left(x \right)}}{\left(x + e\right) \log{\left(x + e \right)}} - \frac{\log{\left(\log{\left(x + e \right)} \right)}}{\sqrt{1 - x^{2}}}\right) \log{\left(x + e \right)}^{\operatorname{acos}{\left(x \right)}}$$
log(E + x)^acos(x)*(-log(log(E + x))/sqrt(1 - x^2) + acos(x)/((E + x)*log(E + x)))
Parte trigonométrica
[src]
acos(x) / log(log(E + x)) acos(x) \
log (E + x)*|- --------------- + ------------------|
| ________ (E + x)*log(E + x)|
| / 2 |
\ \/ 1 - x /
$$\left(\frac{\operatorname{acos}{\left(x \right)}}{\left(x + e\right) \log{\left(x + e \right)}} - \frac{\log{\left(\log{\left(x + e \right)} \right)}}{\sqrt{1 - x^{2}}}\right) \log{\left(x + e \right)}^{\operatorname{acos}{\left(x \right)}}$$
acos(x) / log(log(x + cosh(1) + sinh(1))) acos(x) \
log (x + cosh(1) + sinh(1))*|- ------------------------------- + --------------------------------------------------|
| ________ (x + cosh(1) + sinh(1))*log(x + cosh(1) + sinh(1))|
| / 2 |
\ \/ 1 - x /
$$\left(\frac{\operatorname{acos}{\left(x \right)}}{\left(x + \sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right) \log{\left(x + \sinh{\left(1 \right)} + \cosh{\left(1 \right)} \right)}} - \frac{\log{\left(\log{\left(x + \sinh{\left(1 \right)} + \cosh{\left(1 \right)} \right)} \right)}}{\sqrt{1 - x^{2}}}\right) \log{\left(x + \sinh{\left(1 \right)} + \cosh{\left(1 \right)} \right)}^{\operatorname{acos}{\left(x \right)}}$$
log(x + cosh(1) + sinh(1))^acos(x)*(-log(log(x + cosh(1) + sinh(1)))/sqrt(1 - x^2) + acos(x)/((x + cosh(1) + sinh(1))*log(x + cosh(1) + sinh(1))))