Sr Examen
¿Cómo vas a descomponer esta cos(x/2)/(x-n^4) expresión en fracciones?
Solución
Ha introducido
[src]
/x\
cos|-|
\2/
------
4
x - n
$$\frac{\cos{\left(\frac{x}{2} \right)}}{- n^{4} + x}$$
cos(x/2)/(x - n^4)
Potencias
[src]
I*x -I*x
--- -----
2 2
e e
---- + ------
2 2
-------------
4
x - n
$$\frac{\frac{e^{\frac{i x}{2}}}{2} + \frac{e^{- \frac{i x}{2}}}{2}}{- n^{4} + x}$$
(exp(i*x/2)/2 + exp(-i*x/2)/2)/(x - n^4)
Parte trigonométrica
[src]
1
---------------
/ 4\ /x\
\x - n /*sec|-|
\2/
$$\frac{1}{\left(- n^{4} + x\right) \sec{\left(\frac{x}{2} \right)}}$$
2/x\
-1 + cot |-|
\4/
----------------------
/ 2/x\\ / 4\
|1 + cot |-||*\x - n /
\ \4//
$$\frac{\cot^{2}{\left(\frac{x}{4} \right)} - 1}{\left(- n^{4} + x\right) \left(\cot^{2}{\left(\frac{x}{4} \right)} + 1\right)}$$
2/x\
1 - tan |-|
\4/
----------------------
/ 2/x\\ / 4\
|1 + tan |-||*\x - n /
\ \4//
$$\frac{1 - \tan^{2}{\left(\frac{x}{4} \right)}}{\left(- n^{4} + x\right) \left(\tan^{2}{\left(\frac{x}{4} \right)} + 1\right)}$$
/pi x\
sin|-- + -|
\2 2/
-----------
4
x - n
$$\frac{\sin{\left(\frac{x}{2} + \frac{\pi}{2} \right)}}{- n^{4} + x}$$
1
--------------------
/ 4\ /pi x\
\x - n /*csc|-- - -|
\2 2/
$$\frac{1}{\left(- n^{4} + x\right) \csc{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}$$
1/((x - n^4)*csc(pi/2 - x/2))