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