Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
cos(x)/log(x)-sin(x)/(x*log(x)^2)
¿Cómo vas a descomponer esta cos(x)/log(x)-sin(x)/(x*log(x)^2) expresión en fracciones?
Solución
Ha introducido
[src]
cos(x) sin(x)
------ - ---------
log(x) 2
x*log (x)
$$\frac{\cos{\left(x \right)}}{\log{\left(x \right)}} - \frac{\sin{\left(x \right)}}{x \log{\left(x \right)}^{2}}$$
cos(x)/log(x) - sin(x)/(x*log(x)^2)
Denominador racional
[src]
2
-log(x)*sin(x) + x*log (x)*cos(x)
---------------------------------
3
x*log (x)
$$\frac{x \log{\left(x \right)}^{2} \cos{\left(x \right)} - \log{\left(x \right)} \sin{\left(x \right)}}{x \log{\left(x \right)}^{3}}$$
(-log(x)*sin(x) + x*log(x)^2*cos(x))/(x*log(x)^3)
Potencias
[src]
I*x -I*x
e e
---- + ----- / -I*x I*x\
2 2 I*\- e + e /
------------ + ------------------
log(x) 2
2*x*log (x)
$$\frac{\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}}{\log{\left(x \right)}} + \frac{i \left(e^{i x} - e^{- i x}\right)}{2 x \log{\left(x \right)}^{2}}$$
(exp(i*x)/2 + exp(-i*x)/2)/log(x) + i*(-exp(-i*x) + exp(i*x))/(2*x*log(x)^2)
Combinatoria
[src]
-sin(x) + x*cos(x)*log(x)
-------------------------
2
x*log (x)
$$\frac{x \log{\left(x \right)} \cos{\left(x \right)} - \sin{\left(x \right)}}{x \log{\left(x \right)}^{2}}$$
(-sin(x) + x*cos(x)*log(x))/(x*log(x)^2)
Unión de expresiones racionales
[src]
-sin(x) + x*cos(x)*log(x)
-------------------------
2
x*log (x)
$$\frac{x \log{\left(x \right)} \cos{\left(x \right)} - \sin{\left(x \right)}}{x \log{\left(x \right)}^{2}}$$
(-sin(x) + x*cos(x)*log(x))/(x*log(x)^2)
Parte trigonométrica
[src]
2/x\ /x\
-1 + cot |-| 2*cot|-|
\2/ \2/
------------ - ----------------------
2/x\ / 2/x\\
1 + cot |-| x*|1 + cot |-||*log(x)
\2/ \ \2//
-------------------------------------
log(x)
$$\frac{\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} - \frac{2 \cot{\left(\frac{x}{2} \right)}}{x \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \log{\left(x \right)}}}{\log{\left(x \right)}}$$
2/x\ /x\
1 - tan |-| 2*tan|-|
\2/ \2/
----------- - ----------------------
2/x\ / 2/x\\
1 + tan |-| x*|1 + tan |-||*log(x)
\2/ \ \2//
------------------------------------
log(x)
$$\frac{\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} - \frac{2 \tan{\left(\frac{x}{2} \right)}}{x \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right) \log{\left(x \right)}}}{\log{\left(x \right)}}$$
/ pi\
cos|x - --|
cos(x) \ 2 /
------ - -----------
log(x) 2
x*log (x)
$$\frac{\cos{\left(x \right)}}{\log{\left(x \right)}} - \frac{\cos{\left(x - \frac{\pi}{2} \right)}}{x \log{\left(x \right)}^{2}}$$
2/x\ /x\
-1 + cot |-| 2*cot|-|
\2/ \2/
-------------------- - -----------------------
/ 2/x\\ / 2/x\\ 2
|1 + cot |-||*log(x) x*|1 + cot |-||*log (x)
\ \2// \ \2//
$$\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \log{\left(x \right)}} - \frac{2 \cot{\left(\frac{x}{2} \right)}}{x \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \log{\left(x \right)}^{2}}$$
sin(x) / pi\
- -------- + sin|x + --|
x*log(x) \ 2 /
------------------------
log(x)
$$\frac{\sin{\left(x + \frac{\pi}{2} \right)} - \frac{\sin{\left(x \right)}}{x \log{\left(x \right)}}}{\log{\left(x \right)}}$$
1 1
------------- - ---------------------
log(x)*sec(x) 2 / pi\
x*log (x)*sec|x - --|
\ 2 /
$$\frac{1}{\log{\left(x \right)} \sec{\left(x \right)}} - \frac{1}{x \log{\left(x \right)}^{2} \sec{\left(x - \frac{\pi}{2} \right)}}$$
/ pi\
sin|x + --|
\ 2 / sin(x)
----------- - ---------
log(x) 2
x*log (x)
$$\frac{\sin{\left(x + \frac{\pi}{2} \right)}}{\log{\left(x \right)}} - \frac{\sin{\left(x \right)}}{x \log{\left(x \right)}^{2}}$$
/ pi\
cos|x - --|
\ 2 /
- ----------- + cos(x)
x*log(x)
----------------------
log(x)
$$\frac{\cos{\left(x \right)} - \frac{\cos{\left(x - \frac{\pi}{2} \right)}}{x \log{\left(x \right)}}}{\log{\left(x \right)}}$$
1 1
------------- - ----------------
log(x)*sec(x) 2
x*csc(x)*log (x)
$$\frac{1}{\log{\left(x \right)} \sec{\left(x \right)}} - \frac{1}{x \log{\left(x \right)}^{2} \csc{\left(x \right)}}$$
1 1
----------- - ---------------
/pi \ x*csc(x)*log(x)
csc|-- - x|
\2 /
-----------------------------
log(x)
$$\frac{\frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}} - \frac{1}{x \log{\left(x \right)} \csc{\left(x \right)}}}{\log{\left(x \right)}}$$
1 1 ------------------ - ---------------- /pi \ 2 csc|-- - x|*log(x) x*csc(x)*log (x) \2 /
$$\frac{1}{\log{\left(x \right)} \csc{\left(- x + \frac{\pi}{2} \right)}} - \frac{1}{x \log{\left(x \right)}^{2} \csc{\left(x \right)}}$$
1 1
------ - --------------------
sec(x) / pi\
x*log(x)*sec|x - --|
\ 2 /
-----------------------------
log(x)
$$\frac{\frac{1}{\sec{\left(x \right)}} - \frac{1}{x \log{\left(x \right)} \sec{\left(x - \frac{\pi}{2} \right)}}}{\log{\left(x \right)}}$$
2/x\ /x\
1 - tan |-| 2*tan|-|
\2/ \2/
-------------------- - -----------------------
/ 2/x\\ / 2/x\\ 2
|1 + tan |-||*log(x) x*|1 + tan |-||*log (x)
\ \2// \ \2//
$$\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right) \log{\left(x \right)}} - \frac{2 \tan{\left(\frac{x}{2} \right)}}{x \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right) \log{\left(x \right)}^{2}}$$
sin(x)
- -------- + cos(x)
x*log(x)
-------------------
log(x)
$$\frac{\cos{\left(x \right)} - \frac{\sin{\left(x \right)}}{x \log{\left(x \right)}}}{\log{\left(x \right)}}$$
(-sin(x)/(x*log(x)) + cos(x))/log(x)
Denominador común
[src]
-sin(x) + x*cos(x)*log(x)
-------------------------
2
x*log (x)
$$\frac{x \log{\left(x \right)} \cos{\left(x \right)} - \sin{\left(x \right)}}{x \log{\left(x \right)}^{2}}$$
(-sin(x) + x*cos(x)*log(x))/(x*log(x)^2)