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