Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
cos(x)*exp(sqrt(sin(x)))/(2*sqrt(sin(x)))
¿Cómo vas a descomponer esta cos(x)*exp(sqrt(sin(x)))/(2*sqrt(sin(x))) expresión en fracciones?
Solución
Ha introducido
[src]
________
\/ sin(x)
cos(x)*e
------------------
________
2*\/ sin(x)
$$\frac{e^{\sqrt{\sin{\left(x \right)}}} \cos{\left(x \right)}}{2 \sqrt{\sin{\left(x \right)}}}$$
(cos(x)*exp(sqrt(sin(x))))/((2*sqrt(sin(x))))
Respuesta numérica
[src]
0.5*sin(x)^(-0.5)*cos(x)*exp(sqrt(sin(x)))
0.5*sin(x)^(-0.5)*cos(x)*exp(sqrt(sin(x)))
Potencias
[src]
_____________________
___ / / -I*x I*x\
\/ 2 *\/ -I*\- e + e /
/ I*x -I*x\ ------------------------------
___ |e e | 2
\/ 2 *|---- + -----|*e
\ 2 2 /
----------------------------------------------------
_____________________
/ / -I*x I*x\
2*\/ -I*\- e + e /
$$\frac{\sqrt{2} \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right) e^{\frac{\sqrt{2} \sqrt{- i \left(e^{i x} - e^{- i x}\right)}}{2}}}{2 \sqrt{- i \left(e^{i x} - e^{- i x}\right)}}$$
sqrt(2)*(exp(i*x)/2 + exp(-i*x)/2)*exp(sqrt(2)*sqrt(-i*(-exp(-i*x) + exp(i*x)))/2)/(2*sqrt(-i*(-exp(-i*x) + exp(i*x))))
Denominador racional
[src]
________
________ \/ sin(x)
\/ sin(x) *cos(x)*e
-----------------------------
2*sin(x)
$$\frac{e^{\sqrt{\sin{\left(x \right)}}} \sqrt{\sin{\left(x \right)}} \cos{\left(x \right)}}{2 \sin{\left(x \right)}}$$
sqrt(sin(x))*cos(x)*exp(sqrt(sin(x)))/(2*sin(x))
Parte trigonométrica
[src]
/ / _____________\ / _____________\\
| | / /x\ | | / /x\ ||
| | / cot|-| | | / cot|-| ||
___ / 2/x\\ | | ___ / \2/ | | ___ / \2/ ||
\/ 2 *|-1 + cot |-||*|cosh|\/ 2 * / ----------- | + sinh|\/ 2 * / ----------- ||
\ \2// | | / 2/x\ | | / 2/x\ ||
| | / 1 + cot |-| | | / 1 + cot |-| ||
\ \ \/ \2/ / \ \/ \2/ //
--------------------------------------------------------------------------------------------
_____________
/ /x\
/ cot|-|
/ \2/ / 2/x\\
4* / ----------- *|1 + cot |-||
/ 2/x\ \ \2//
/ 1 + cot |-|
\/ \2/
$$\frac{\sqrt{2} \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right) \left(\sinh{\left(\sqrt{2} \sqrt{\frac{\cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}} \right)} + \cosh{\left(\sqrt{2} \sqrt{\frac{\cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}} \right)}\right)}{4 \sqrt{\frac{\cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}} \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)}$$
________
/ 1
/ ------
\/ csc(x)
e
--------------------------
________
/ 1 /pi \
2* / ------ *csc|-- - x|
\/ csc(x) \2 /
$$\frac{e^{\sqrt{\frac{1}{\csc{\left(x \right)}}}}}{2 \sqrt{\frac{1}{\csc{\left(x \right)}}} \csc{\left(- x + \frac{\pi}{2} \right)}}$$
/ / _____________\ / _____________\\
| | / /x\ | | / /x\ ||
| | / tan|-| | | / tan|-| ||
___ / 2/x\\ | | ___ / \2/ | | ___ / \2/ ||
\/ 2 *|1 - tan |-||*|cosh|\/ 2 * / ----------- | + sinh|\/ 2 * / ----------- ||
\ \2// | | / 2/x\ | | / 2/x\ ||
| | / 1 + tan |-| | | / 1 + tan |-| ||
\ \ \/ \2/ / \ \/ \2/ //
-------------------------------------------------------------------------------------------
_____________
/ /x\
/ tan|-|
/ \2/ / 2/x\\
4* / ----------- *|1 + tan |-||
/ 2/x\ \ \2//
/ 1 + tan |-|
\/ \2/
$$\frac{\sqrt{2} \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) \left(\sinh{\left(\sqrt{2} \sqrt{\frac{\tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}} \right)} + \cosh{\left(\sqrt{2} \sqrt{\frac{\tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}} \right)}\right)}{4 \sqrt{\frac{\tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}} \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}$$
2/x\ / 2/x\\ / / ________\ / ________\\
-cos |-|*|-1 + tan |-||*\cosh\\/ sin(x) / + sinh\\/ sin(x) //
\2/ \ \2//
--------------------------------------------------------------
________
2*\/ sin(x)
$$- \frac{\left(\tan^{2}{\left(\frac{x}{2} \right)} - 1\right) \left(\sinh{\left(\sqrt{\sin{\left(x \right)}} \right)} + \cosh{\left(\sqrt{\sin{\left(x \right)}} \right)}\right) \cos^{2}{\left(\frac{x}{2} \right)}}{2 \sqrt{\sin{\left(x \right)}}}$$
_____________
/ /x\
/ cot|-|
___ / \2/
\/ 2 * / -----------
/ 2/x\
/ 1 + cot |-|
___ / 2/x\\ \/ \2/
\/ 2 *|-1 + cot |-||*e
\ \2//
-------------------------------------------------
_____________
/ /x\
/ cot|-|
/ \2/ / 2/x\\
4* / ----------- *|1 + cot |-||
/ 2/x\ \ \2//
/ 1 + cot |-|
\/ \2/
$$\frac{\sqrt{2} \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right) e^{\sqrt{2} \sqrt{\frac{\cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}}}}{4 \sqrt{\frac{\cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}} \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)}$$
/ / ________\ / ________\\ / pi\
\cosh\\/ sin(x) / + sinh\\/ sin(x) //*sin|x + --|
\ 2 /
-------------------------------------------------
________
2*\/ sin(x)
$$\frac{\left(\sinh{\left(\sqrt{\sin{\left(x \right)}} \right)} + \cosh{\left(\sqrt{\sin{\left(x \right)}} \right)}\right) \sin{\left(x + \frac{\pi}{2} \right)}}{2 \sqrt{\sin{\left(x \right)}}}$$
_____________
/ /x\
/ tan|-|
___ / \2/
\/ 2 * / -----------
/ 2/x\
/ 1 + tan |-|
___ / 2/x\\ \/ \2/
\/ 2 *|1 - tan |-||*e
\ \2//
------------------------------------------------
_____________
/ /x\
/ tan|-|
/ \2/ / 2/x\\
4* / ----------- *|1 + tan |-||
/ 2/x\ \ \2//
/ 1 + tan |-|
\/ \2/
$$\frac{\sqrt{2} \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) e^{\sqrt{2} \sqrt{\frac{\tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}}}}{4 \sqrt{\frac{\tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}} \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}$$
/ ________\ / ________\
| / 1 | | / 1 |
cosh| / ------ | + sinh| / ------ |
\\/ csc(x) / \\/ csc(x) /
---------------------------------------
________
/ 1 /pi \
2* / ------ *csc|-- - x|
\/ csc(x) \2 /
$$\frac{\sinh{\left(\sqrt{\frac{1}{\csc{\left(x \right)}}} \right)} + \cosh{\left(\sqrt{\frac{1}{\csc{\left(x \right)}}} \right)}}{2 \sqrt{\frac{1}{\csc{\left(x \right)}}} \csc{\left(- x + \frac{\pi}{2} \right)}}$$
/ / ________\ / ________\\
\cosh\\/ sin(x) / + sinh\\/ sin(x) //*cos(x)
--------------------------------------------
________
2*\/ sin(x)
$$\frac{\left(\sinh{\left(\sqrt{\sin{\left(x \right)}} \right)} + \cosh{\left(\sqrt{\sin{\left(x \right)}} \right)}\right) \cos{\left(x \right)}}{2 \sqrt{\sin{\left(x \right)}}}$$
_____________
/ 1
/ -----------
/ / pi\
/ sec|x - --|
\/ \ 2 /
e
----------------------------
_____________
/ 1
2* / ----------- *sec(x)
/ / pi\
/ sec|x - --|
\/ \ 2 /
$$\frac{e^{\sqrt{\frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}}}}{2 \sqrt{\frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}} \sec{\left(x \right)}}$$
/ _____________\ / _____________\
| / 1 | | / 1 |
cosh| / ----------- | + sinh| / ----------- |
| / / pi\ | | / / pi\ |
| / sec|x - --| | | / sec|x - --| |
\\/ \ 2 / / \\/ \ 2 / /
-----------------------------------------------------
_____________
/ 1
2* / ----------- *sec(x)
/ / pi\
/ sec|x - --|
\/ \ 2 /
$$\frac{\sinh{\left(\sqrt{\frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}} \right)} + \cosh{\left(\sqrt{\frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}} \right)}}{2 \sqrt{\frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}} \sec{\left(x \right)}}$$
________
/ 1
/ ------
\/ csc(x)
e
---------------------
________
/ 1
2* / ------ *sec(x)
\/ csc(x)
$$\frac{e^{\sqrt{\frac{1}{\csc{\left(x \right)}}}}}{2 \sqrt{\frac{1}{\csc{\left(x \right)}}} \sec{\left(x \right)}}$$
2/x\ / 2/x\\ / / ________\ / ________\\
sin |-|*|-1 + cot |-||*\cosh\\/ sin(x) / + sinh\\/ sin(x) //
\2/ \ \2//
------------------------------------------------------------
________
2*\/ sin(x)
$$\frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right) \left(\sinh{\left(\sqrt{\sin{\left(x \right)}} \right)} + \cosh{\left(\sqrt{\sin{\left(x \right)}} \right)}\right) \sin^{2}{\left(\frac{x}{2} \right)}}{2 \sqrt{\sin{\left(x \right)}}}$$
/ / _____________\ / _____________\\
| | / / pi\ | | / / pi\ ||
|cosh| / cos|x - --| | + sinh| / cos|x - --| ||*cos(x)
\ \\/ \ 2 / / \\/ \ 2 / //
----------------------------------------------------------
_____________
/ / pi\
2* / cos|x - --|
\/ \ 2 /
$$\frac{\left(\sinh{\left(\sqrt{\cos{\left(x - \frac{\pi}{2} \right)}} \right)} + \cosh{\left(\sqrt{\cos{\left(x - \frac{\pi}{2} \right)}} \right)}\right) \cos{\left(x \right)}}{2 \sqrt{\cos{\left(x - \frac{\pi}{2} \right)}}}$$
(cosh(sqrt(cos(x - pi/2))) + sinh(sqrt(cos(x - pi/2))))*cos(x)/(2*sqrt(cos(x - pi/2)))