Sr Examen
¿Cómo vas a descomponer esta cos(x-sin(x))/(4*x-pi) expresión en fracciones?
Solución
Ha introducido
[src]
cos(x - sin(x))
---------------
4*x - pi
$$\frac{\cos{\left(x - \sin{\left(x \right)} \right)}}{4 x - \pi}$$
cos(x - sin(x))/(4*x - pi)
Respuesta numérica
[src]
cos(x - sin(x))/(-3.14159265358979 + 4.0*x)
cos(x - sin(x))/(-3.14159265358979 + 4.0*x)
Potencias
[src]
/ / -I*x I*x\\ / / -I*x I*x\\
| I*\- e + e /| | I*\- e + e /|
I*|x + ------------------| I*|-x - ------------------|
\ 2 / \ 2 /
e e
--------------------------- + ----------------------------
2 2
----------------------------------------------------------
-pi + 4*x
$$\frac{\frac{e^{i \left(- x - \frac{i \left(e^{i x} - e^{- i x}\right)}{2}\right)}}{2} + \frac{e^{i \left(x + \frac{i \left(e^{i x} - e^{- i x}\right)}{2}\right)}}{2}}{4 x - \pi}$$
(exp(i*(x + i*(-exp(-i*x) + exp(i*x))/2))/2 + exp(i*(-x - i*(-exp(-i*x) + exp(i*x))/2))/2)/(-pi + 4*x)
Parte trigonométrica
[src]
1
--------------------------------
/ 1 \
(-pi + 4*x)*sec|x - -----------|
| /pi \|
| sec|-- - x||
\ \2 //
$$\frac{1}{\left(4 x - \pi\right) \sec{\left(x - \frac{1}{\sec{\left(- x + \frac{\pi}{2} \right)}} \right)}}$$
/ / pi\\
cos|x - cos|x - --||
\ \ 2 //
--------------------
-pi + 4*x
$$\frac{\cos{\left(x - \cos{\left(x - \frac{\pi}{2} \right)} \right)}}{4 x - \pi}$$
/ pi \
sin|x + -- - sin(x)|
\ 2 /
--------------------
-pi + 4*x
$$\frac{\sin{\left(x - \sin{\left(x \right)} + \frac{\pi}{2} \right)}}{4 x - \pi}$$
/ /x\ \
| cot|-| |
2|x \2/ |
-1 + cot |- - -----------|
|2 2/x\|
| 1 + cot |-||
\ \2//
---------------------------------------
/ / /x\ \\
| | cot|-| ||
| 2|x \2/ ||
|1 + cot |- - -----------||*(-pi + 4*x)
| |2 2/x\||
| | 1 + cot |-|||
\ \ \2///
$$\frac{\cot^{2}{\left(\frac{x}{2} - \frac{\cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} \right)} - 1}{\left(4 x - \pi\right) \left(\cot^{2}{\left(\frac{x}{2} - \frac{\cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} \right)} + 1\right)}$$
/ /x\ \
| tan|-| |
2|x \2/ |
1 - tan |- - -----------|
|2 2/x\|
| 1 + tan |-||
\ \2//
---------------------------------------
/ / /x\ \\
| | tan|-| ||
| 2|x \2/ ||
|1 + tan |- - -----------||*(-pi + 4*x)
| |2 2/x\||
| | 1 + tan |-|||
\ \ \2///
$$\frac{1 - \tan^{2}{\left(\frac{x}{2} - \frac{\tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} \right)}}{\left(4 x - \pi\right) \left(\tan^{2}{\left(\frac{x}{2} - \frac{\tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} \right)} + 1\right)}$$
1
--------------------------------
/ 1 \
(-pi + 4*x)*sec|x - -----------|
| / pi\|
| sec|x - --||
\ \ 2 //
$$\frac{1}{\left(4 x - \pi\right) \sec{\left(x - \frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}} \right)}}$$
1
--------------------------------
/ 1 pi \
(-pi + 4*x)*csc|------ + -- - x|
\csc(x) 2 /
$$\frac{1}{\left(4 x - \pi\right) \csc{\left(- x + \frac{\pi}{2} + \frac{1}{\csc{\left(x \right)}} \right)}}$$
1
---------------------------
/ 1 \
(-pi + 4*x)*sec|x - ------|
\ csc(x)/
$$\frac{1}{\left(4 x - \pi\right) \sec{\left(x - \frac{1}{\csc{\left(x \right)}} \right)}}$$
1/((-pi + 4*x)*sec(x - 1/csc(x)))