Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
sqrt(x*cos(2*x))*(cos(2*x)/2-x*sin(2*x))/(x*cos(2*x))
¿Cómo vas a descomponer esta sqrt(x*cos(2*x))*(cos(2*x)/2-x*sin(2*x))/(x*cos(2*x)) expresión en fracciones?
Solución
Ha introducido
[src]
____________ /cos(2*x) \
\/ x*cos(2*x) *|-------- - x*sin(2*x)|
\ 2 /
--------------------------------------
x*cos(2*x)
$$\frac{\sqrt{x \cos{\left(2 x \right)}} \left(- x \sin{\left(2 x \right)} + \frac{\cos{\left(2 x \right)}}{2}\right)}{x \cos{\left(2 x \right)}}$$
(sqrt(x*cos(2*x))*(cos(2*x)/2 - x*sin(2*x)))/((x*cos(2*x)))
Simplificación general
[src]
cos(2*x)
-------- - x*sin(2*x)
2
---------------------
____________
\/ x*cos(2*x)
$$\frac{- x \sin{\left(2 x \right)} + \frac{\cos{\left(2 x \right)}}{2}}{\sqrt{x \cos{\left(2 x \right)}}}$$
(cos(2*x)/2 - x*sin(2*x))/sqrt(x*cos(2*x))
Denominador racional
[src]
____________
\/ x*cos(2*x) *(-2*x*sin(2*x) + cos(2*x))
-----------------------------------------
2*x*cos(2*x)
$$\frac{\sqrt{x \cos{\left(2 x \right)}} \left(- 2 x \sin{\left(2 x \right)} + \cos{\left(2 x \right)}\right)}{2 x \cos{\left(2 x \right)}}$$
sqrt(x*cos(2*x))*(-2*x*sin(2*x) + cos(2*x))/(2*x*cos(2*x))
Unión de expresiones racionales
[src]
____________
\/ x*cos(2*x) *(-2*x*sin(2*x) + cos(2*x))
-----------------------------------------
2*x*cos(2*x)
$$\frac{\sqrt{x \cos{\left(2 x \right)}} \left(- 2 x \sin{\left(2 x \right)} + \cos{\left(2 x \right)}\right)}{2 x \cos{\left(2 x \right)}}$$
sqrt(x*cos(2*x))*(-2*x*sin(2*x) + cos(2*x))/(2*x*cos(2*x))
Potencias
[src]
______________________
/ / -2*I*x 2*I*x\ / -2*I*x 2*I*x / -2*I*x 2*I*x\\
/ |e e | |e e I*x*\- e + e /|
/ x*|------- + ------| *|------- + ------ + ------------------------|
\/ \ 2 2 / \ 4 4 2 /
-------------------------------------------------------------------------
/ -2*I*x 2*I*x\
|e e |
x*|------- + ------|
\ 2 2 /
$$\frac{\sqrt{x \left(\frac{e^{2 i x}}{2} + \frac{e^{- 2 i x}}{2}\right)} \left(\frac{i x \left(e^{2 i x} - e^{- 2 i x}\right)}{2} + \frac{e^{2 i x}}{4} + \frac{e^{- 2 i x}}{4}\right)}{x \left(\frac{e^{2 i x}}{2} + \frac{e^{- 2 i x}}{2}\right)}$$
sqrt(x*(exp(-2*i*x)/2 + exp(2*i*x)/2))*(exp(-2*i*x)/4 + exp(2*i*x)/4 + i*x*(-exp(-2*i*x) + exp(2*i*x))/2)/(x*(exp(-2*i*x)/2 + exp(2*i*x)/2))
Combinatoria
[src]
____________
-\/ x*cos(2*x) *(-cos(2*x) + 2*x*sin(2*x))
-------------------------------------------
2*x*cos(2*x)
$$- \frac{\sqrt{x \cos{\left(2 x \right)}} \left(2 x \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right)}{2 x \cos{\left(2 x \right)}}$$
-sqrt(x*cos(2*x))*(-cos(2*x) + 2*x*sin(2*x))/(2*x*cos(2*x))
Denominador común
[src]
/ ____________ ____________ \
-\- \/ x*cos(2*x) *cos(2*x) + 2*x*\/ x*cos(2*x) *sin(2*x)/
-----------------------------------------------------------
2*x*cos(2*x)
$$- \frac{2 x \sqrt{x \cos{\left(2 x \right)}} \sin{\left(2 x \right)} - \sqrt{x \cos{\left(2 x \right)}} \cos{\left(2 x \right)}}{2 x \cos{\left(2 x \right)}}$$
-(-sqrt(x*cos(2*x))*cos(2*x) + 2*x*sqrt(x*cos(2*x))*sin(2*x))/(2*x*cos(2*x))
Parte trigonométrica
[src]
__________
/ x 2 / 1 x \
/ -------- *sec (x)*|---------- - -------------|
\/ sec(2*x) |2*sec(2*x) / pi\|
| sec|2*x - --||
\ \ 2 //
---------------------------------------------------
/ 2 \
| sec (x) |
x*|1 - ------------|
| 2/ pi\|
| sec |x - --||
\ \ 2 //
$$\frac{\sqrt{\frac{x}{\sec{\left(2 x \right)}}} \left(- \frac{x}{\sec{\left(2 x - \frac{\pi}{2} \right)}} + \frac{1}{2 \sec{\left(2 x \right)}}\right) \sec^{2}{\left(x \right)}}{x \left(- \frac{\sec^{2}{\left(x \right)}}{\sec^{2}{\left(x - \frac{\pi}{2} \right)}} + 1\right)}$$
/ /pi \ \
_________________ |sin|-- + 2*x| |
/ /pi \ | \2 / |
/ x*sin|-- + 2*x| *|------------- - x*sin(2*x)|
\/ \2 / \ 2 /
--------------------------------------------------
/pi \
x*sin|-- + 2*x|
\2 /
$$\frac{\sqrt{x \sin{\left(2 x + \frac{\pi}{2} \right)}} \left(- x \sin{\left(2 x \right)} + \frac{\sin{\left(2 x + \frac{\pi}{2} \right)}}{2}\right)}{x \sin{\left(2 x + \frac{\pi}{2} \right)}}$$
____________
\/ x*cos(2*x) *(1/2 - x*tan(2*x))
---------------------------------
x
$$\frac{\sqrt{x \cos{\left(2 x \right)}} \left(- x \tan{\left(2 x \right)} + \frac{1}{2}\right)}{x}$$
_________________
/ / 2 \ / 2 \
/ x*\1 - tan (x)/ / 2 \ | 1 - tan (x) 2*x*tan(x)|
/ --------------- *\1 + tan (x)/*|--------------- - -----------|
/ 2 | / 2 \ 2 |
\/ 1 + tan (x) \2*\1 + tan (x)/ 1 + tan (x)/
---------------------------------------------------------------------
/ 2 \
x*\1 - tan (x)/
$$\frac{\sqrt{\frac{x \left(1 - \tan^{2}{\left(x \right)}\right)}{\tan^{2}{\left(x \right)} + 1}} \left(- \frac{2 x \tan{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1} + \frac{1 - \tan^{2}{\left(x \right)}}{2 \left(\tan^{2}{\left(x \right)} + 1\right)}\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{x \left(1 - \tan^{2}{\left(x \right)}\right)}$$
__________
/ x / 1 x \
/ -------- *|---------- - -------------|*sec(2*x)
\/ sec(2*x) |2*sec(2*x) / pi\|
| sec|2*x - --||
\ \ 2 //
----------------------------------------------------
x
$$\frac{\sqrt{\frac{x}{\sec{\left(2 x \right)}}} \left(- \frac{x}{\sec{\left(2 x - \frac{\pi}{2} \right)}} + \frac{1}{2 \sec{\left(2 x \right)}}\right) \sec{\left(2 x \right)}}{x}$$
__________
/ x / 1 x \
/ -------- *|---------- - --------|*sec(2*x)
\/ sec(2*x) \2*sec(2*x) csc(2*x)/
-----------------------------------------------
x
$$\frac{\sqrt{\frac{x}{\sec{\left(2 x \right)}}} \left(- \frac{x}{\csc{\left(2 x \right)}} + \frac{1}{2 \sec{\left(2 x \right)}}\right) \sec{\left(2 x \right)}}{x}$$
_________________
/ / 2 \
/ x*\1 - tan (x)/
/ --------------- *(1/2 - x*tan(2*x))
/ 2
\/ 1 + tan (x)
------------------------------------------
x
$$\frac{\sqrt{\frac{x \left(1 - \tan^{2}{\left(x \right)}\right)}{\tan^{2}{\left(x \right)} + 1}} \left(- x \tan{\left(2 x \right)} + \frac{1}{2}\right)}{x}$$
__________
/ x 2/ pi\ / 1 x \
/ -------- *sec |x - --|*|---------- - -------------|
\/ sec(2*x) \ 2 / |2*sec(2*x) / pi\|
| sec|2*x - --||
\ \ 2 //
--------------------------------------------------------
/ 2/ pi\\
| sec |x - --||
| \ 2 /|
x*|-1 + ------------|
| 2 |
\ sec (x) /
$$\frac{\sqrt{\frac{x}{\sec{\left(2 x \right)}}} \left(- \frac{x}{\sec{\left(2 x - \frac{\pi}{2} \right)}} + \frac{1}{2 \sec{\left(2 x \right)}}\right) \sec^{2}{\left(x - \frac{\pi}{2} \right)}}{x \left(-1 + \frac{\sec^{2}{\left(x - \frac{\pi}{2} \right)}}{\sec^{2}{\left(x \right)}}\right)}$$
/ / pi\\
| x*cos|2*x - --||
____________ |1 \ 2 /|
\/ x*cos(2*x) *|- - ---------------|
\2 cos(2*x) /
------------------------------------
x
$$\frac{\sqrt{x \cos{\left(2 x \right)}} \left(- \frac{x \cos{\left(2 x - \frac{\pi}{2} \right)}}{\cos{\left(2 x \right)}} + \frac{1}{2}\right)}{x}$$
__________________
/ / 2 \
/ x*\-1 + cot (x)/ /1 x \
/ ---------------- *|- - --------|
/ 2 \2 cot(2*x)/
\/ 1 + cot (x)
---------------------------------------
x
$$\frac{\sqrt{\frac{x \left(\cot^{2}{\left(x \right)} - 1\right)}{\cot^{2}{\left(x \right)} + 1}} \left(- \frac{x}{\cot{\left(2 x \right)}} + \frac{1}{2}\right)}{x}$$
____________ /cos(2*x) \
\/ x*cos(2*x) *|-------- - x*sin(2*x)|
\ 2 /
--------------------------------------
/ 2 \ 2
x*\1 - tan (x)/*cos (x)
$$\frac{\sqrt{x \cos{\left(2 x \right)}} \left(- x \sin{\left(2 x \right)} + \frac{\cos{\left(2 x \right)}}{2}\right)}{x \left(1 - \tan^{2}{\left(x \right)}\right) \cos^{2}{\left(x \right)}}$$
____________ 2/x\ /cos(2*x) \
\/ x*cos(2*x) *tan |-|*|-------- - x*sin(2*x)|
\2/ \ 2 /
----------------------------------------------
/ 2 \ 4/x\
4*x*\-1 + cot (x)/*sin |-|
\2/
$$\frac{\sqrt{x \cos{\left(2 x \right)}} \left(- x \sin{\left(2 x \right)} + \frac{\cos{\left(2 x \right)}}{2}\right) \tan^{2}{\left(\frac{x}{2} \right)}}{4 x \left(\cot^{2}{\left(x \right)} - 1\right) \sin^{4}{\left(\frac{x}{2} \right)}}$$
__________
/ x /1 x*sec(2*x) \
/ -------- *|- - -------------|
\/ sec(2*x) |2 / pi\|
| sec|2*x - --||
\ \ 2 //
----------------------------------
x
$$\frac{\sqrt{\frac{x}{\sec{\left(2 x \right)}}} \left(- \frac{x \sec{\left(2 x \right)}}{\sec{\left(2 x - \frac{\pi}{2} \right)}} + \frac{1}{2}\right)}{x}$$
____________ 2 /cos(2*x) \
\/ x*cos(2*x) *csc (x)*|-------- - x*sin(2*x)|
\ 2 /
----------------------------------------------
/ 1 \
x*|-1 + -------|
| 2 |
\ tan (x)/
$$\frac{\sqrt{x \cos{\left(2 x \right)}} \left(- x \sin{\left(2 x \right)} + \frac{\cos{\left(2 x \right)}}{2}\right) \csc^{2}{\left(x \right)}}{x \left(-1 + \frac{1}{\tan^{2}{\left(x \right)}}\right)}$$
____________ /cos(2*x) / pi\\
\/ x*cos(2*x) *|-------- - x*cos|2*x - --||
\ 2 \ 2 //
-------------------------------------------
/ 2 \
| cos (x) | 2/ pi\
x*|-1 + ------------|*cos |x - --|
| 2/ pi\| \ 2 /
| cos |x - --||
\ \ 2 //
$$\frac{\sqrt{x \cos{\left(2 x \right)}} \left(- x \cos{\left(2 x - \frac{\pi}{2} \right)} + \frac{\cos{\left(2 x \right)}}{2}\right)}{x \left(\frac{\cos^{2}{\left(x \right)}}{\cos^{2}{\left(x - \frac{\pi}{2} \right)}} - 1\right) \cos^{2}{\left(x - \frac{\pi}{2} \right)}}$$
_______________
/ x / 1 x \ /pi \
/ ------------- *|--------------- - --------|*csc|-- - 2*x|
/ /pi \ | /pi \ csc(2*x)| \2 /
/ csc|-- - 2*x| |2*csc|-- - 2*x| |
\/ \2 / \ \2 / /
----------------------------------------------------------------
x
$$\frac{\sqrt{\frac{x}{\csc{\left(- 2 x + \frac{\pi}{2} \right)}}} \left(- \frac{x}{\csc{\left(2 x \right)}} + \frac{1}{2 \csc{\left(- 2 x + \frac{\pi}{2} \right)}}\right) \csc{\left(- 2 x + \frac{\pi}{2} \right)}}{x}$$
____________ 2 /cos(2*x) \
\/ x*cos(2*x) *sec (x)*|-------- - x*sin(2*x)|
\ 2 /
----------------------------------------------
/ 2 \
x*\1 - tan (x)/
$$\frac{\sqrt{x \cos{\left(2 x \right)}} \left(- x \sin{\left(2 x \right)} + \frac{\cos{\left(2 x \right)}}{2}\right) \sec^{2}{\left(x \right)}}{x \left(1 - \tan^{2}{\left(x \right)}\right)}$$
____________ /cos(2*x) \
\/ x*cos(2*x) *|-------- - x*sin(2*x)|
\ 2 /
---------------------------------------
2
/ 2 \ / 2/x\\ 4/x\
x*\1 - tan (x)/*|-1 + cot |-|| *sin |-|
\ \2// \2/
$$\frac{\sqrt{x \cos{\left(2 x \right)}} \left(- x \sin{\left(2 x \right)} + \frac{\cos{\left(2 x \right)}}{2}\right)}{x \left(1 - \tan^{2}{\left(x \right)}\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{2} \sin^{4}{\left(\frac{x}{2} \right)}}$$
____________ /cos(2*x) / pi\\
\/ x*cos(2*x) *|-------- - x*cos|2*x - --||
\ 2 \ 2 //
-------------------------------------------
/ 2/ pi\\
| cos |x - --||
| \ 2 /| 2
x*|1 - ------------|*cos (x)
| 2 |
\ cos (x) /
$$\frac{\sqrt{x \cos{\left(2 x \right)}} \left(- x \cos{\left(2 x - \frac{\pi}{2} \right)} + \frac{\cos{\left(2 x \right)}}{2}\right)}{x \left(1 - \frac{\cos^{2}{\left(x - \frac{\pi}{2} \right)}}{\cos^{2}{\left(x \right)}}\right) \cos^{2}{\left(x \right)}}$$
____________ /cos(2*x) \
\/ x*cos(2*x) *|-------- - x*sin(2*x)|
\ 2 /
--------------------------------------
/ 1 \ 2
x*|-1 + -------|*sin (x)
| 2 |
\ tan (x)/
$$\frac{\sqrt{x \cos{\left(2 x \right)}} \left(- x \sin{\left(2 x \right)} + \frac{\cos{\left(2 x \right)}}{2}\right)}{x \left(-1 + \frac{1}{\tan^{2}{\left(x \right)}}\right) \sin^{2}{\left(x \right)}}$$
/ /pi \ \
_________________ |sin|-- + 2*x| |
/ /pi \ | \2 / |
/ x*sin|-- + 2*x| *|------------- - x*sin(2*x)|
\/ \2 / \ 2 /
--------------------------------------------------
/ 4 \
| 4*sin (x)| 2/ pi\
x*|1 - ---------|*sin |x + --|
| 2 | \ 2 /
\ sin (2*x)/
$$\frac{\sqrt{x \sin{\left(2 x + \frac{\pi}{2} \right)}} \left(- x \sin{\left(2 x \right)} + \frac{\sin{\left(2 x + \frac{\pi}{2} \right)}}{2}\right)}{x \left(- \frac{4 \sin^{4}{\left(x \right)}}{\sin^{2}{\left(2 x \right)}} + 1\right) \sin^{2}{\left(x + \frac{\pi}{2} \right)}}$$
_______________
/ x 2 / 1 x \
/ ------------- *csc (x)*|--------------- - --------|
/ /pi \ | /pi \ csc(2*x)|
/ csc|-- - 2*x| |2*csc|-- - 2*x| |
\/ \2 / \ \2 / /
----------------------------------------------------------
/ 2 \
| csc (x) |
x*|-1 + ------------|
| 2/pi \|
| csc |-- - x||
\ \2 //
$$\frac{\sqrt{\frac{x}{\csc{\left(- 2 x + \frac{\pi}{2} \right)}}} \left(- \frac{x}{\csc{\left(2 x \right)}} + \frac{1}{2 \csc{\left(- 2 x + \frac{\pi}{2} \right)}}\right) \csc^{2}{\left(x \right)}}{x \left(\frac{\csc^{2}{\left(x \right)}}{\csc^{2}{\left(- x + \frac{\pi}{2} \right)}} - 1\right)}$$
____________ /cos(2*x) / pi\\
\/ x*cos(2*x) *|-------- - x*cos|2*x - --||
\ 2 \ 2 //
-------------------------------------------
x*cos(2*x)
$$\frac{\sqrt{x \cos{\left(2 x \right)}} \left(- x \cos{\left(2 x - \frac{\pi}{2} \right)} + \frac{\cos{\left(2 x \right)}}{2}\right)}{x \cos{\left(2 x \right)}}$$
_________________
/ / 2 \ 2 / 2 \
/ x*\1 - tan (x)/ / 2/x\\ | 1 - tan (x) 2*x*tan(x)|
/ --------------- *|1 + tan |-|| *|--------------- - -----------|
/ 2 \ \2// | / 2 \ 2 |
\/ 1 + tan (x) \2*\1 + tan (x)/ 1 + tan (x)/
----------------------------------------------------------------------
2
/ 2 \ / 2/x\\
x*\1 - tan (x)/*|1 - tan |-||
\ \2//
$$\frac{\sqrt{\frac{x \left(1 - \tan^{2}{\left(x \right)}\right)}{\tan^{2}{\left(x \right)} + 1}} \left(- \frac{2 x \tan{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1} + \frac{1 - \tan^{2}{\left(x \right)}}{2 \left(\tan^{2}{\left(x \right)} + 1\right)}\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}{x \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{2} \left(1 - \tan^{2}{\left(x \right)}\right)}$$
__________________
/ / 2 \ / 2 \
/ x*\-1 + cot (x)/ / 2 \ | -1 + cot (x) 2*x*cot(x)|
/ ---------------- *\1 + cot (x)/*|--------------- - -----------|
/ 2 | / 2 \ 2 |
\/ 1 + cot (x) \2*\1 + cot (x)/ 1 + cot (x)/
----------------------------------------------------------------------
/ 2 \
x*\-1 + cot (x)/
$$\frac{\sqrt{\frac{x \left(\cot^{2}{\left(x \right)} - 1\right)}{\cot^{2}{\left(x \right)} + 1}} \left(- \frac{2 x \cot{\left(x \right)}}{\cot^{2}{\left(x \right)} + 1} + \frac{\cot^{2}{\left(x \right)} - 1}{2 \left(\cot^{2}{\left(x \right)} + 1\right)}\right) \left(\cot^{2}{\left(x \right)} + 1\right)}{x \left(\cot^{2}{\left(x \right)} - 1\right)}$$
_________________ / 2 \
/ /pi \ |1 2*x*sin (2*x)|
/ x*sin|-- + 2*x| *|- - -------------|
\/ \2 / \2 sin(4*x) /
-----------------------------------------
x
$$\frac{\sqrt{x \sin{\left(2 x + \frac{\pi}{2} \right)}} \left(- \frac{2 x \sin^{2}{\left(2 x \right)}}{\sin{\left(4 x \right)}} + \frac{1}{2}\right)}{x}$$
__________________
/ / 2 \ 2 / 2 \
/ x*\-1 + cot (x)/ / 2/x\\ | -1 + cot (x) 2*x*cot(x)|
/ ---------------- *|1 + cot |-|| *|--------------- - -----------|
/ 2 \ \2// | / 2 \ 2 |
\/ 1 + cot (x) \2*\1 + cot (x)/ 1 + cot (x)/
-----------------------------------------------------------------------
/ 2 \ 2/x\
4*x*\-1 + cot (x)/*cot |-|
\2/
$$\frac{\sqrt{\frac{x \left(\cot^{2}{\left(x \right)} - 1\right)}{\cot^{2}{\left(x \right)} + 1}} \left(- \frac{2 x \cot{\left(x \right)}}{\cot^{2}{\left(x \right)} + 1} + \frac{\cot^{2}{\left(x \right)} - 1}{2 \left(\cot^{2}{\left(x \right)} + 1\right)}\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}{4 x \left(\cot^{2}{\left(x \right)} - 1\right) \cot^{2}{\left(\frac{x}{2} \right)}}$$
____________ /cos(2*x) \
\/ x*cos(2*x) *|-------- - x*sin(2*x)|
\ 2 /
--------------------------------------
/ 2 \ 2
x*\-1 + cot (x)/*sin (x)
$$\frac{\sqrt{x \cos{\left(2 x \right)}} \left(- x \sin{\left(2 x \right)} + \frac{\cos{\left(2 x \right)}}{2}\right)}{x \left(\cot^{2}{\left(x \right)} - 1\right) \sin^{2}{\left(x \right)}}$$
____________ /cos(2*x) \
\/ x*cos(2*x) *|-------- - x*sin(2*x)|
\ 2 /
--------------------------------------
/ 1 \ 4/x\ 2/x\
4*x*|-1 + -------|*cos |-|*tan |-|
| 2 | \2/ \2/
\ tan (x)/
$$\frac{\sqrt{x \cos{\left(2 x \right)}} \left(- x \sin{\left(2 x \right)} + \frac{\cos{\left(2 x \right)}}{2}\right)}{4 x \left(-1 + \frac{1}{\tan^{2}{\left(x \right)}}\right) \cos^{4}{\left(\frac{x}{2} \right)} \tan^{2}{\left(\frac{x}{2} \right)}}$$
_______________
/ x 2/pi \ / 1 x \
/ ------------- *csc |-- - x|*|--------------- - --------|
/ /pi \ \2 / | /pi \ csc(2*x)|
/ csc|-- - 2*x| |2*csc|-- - 2*x| |
\/ \2 / \ \2 / /
---------------------------------------------------------------
/ 2/pi \\
| csc |-- - x||
| \2 /|
x*|1 - ------------|
| 2 |
\ csc (x) /
$$\frac{\sqrt{\frac{x}{\csc{\left(- 2 x + \frac{\pi}{2} \right)}}} \left(- \frac{x}{\csc{\left(2 x \right)}} + \frac{1}{2 \csc{\left(- 2 x + \frac{\pi}{2} \right)}}\right) \csc^{2}{\left(- x + \frac{\pi}{2} \right)}}{x \left(1 - \frac{\csc^{2}{\left(- x + \frac{\pi}{2} \right)}}{\csc^{2}{\left(x \right)}}\right)}$$
cos(2*x)
-------- - x*sin(2*x)
2
---------------------
____________
\/ x*cos(2*x)
$$\frac{- x \sin{\left(2 x \right)} + \frac{\cos{\left(2 x \right)}}{2}}{\sqrt{x \cos{\left(2 x \right)}}}$$
/ /pi \\
_______________ | x*csc|-- - 2*x||
/ x |1 \2 /|
/ ------------- *|- - ---------------|
/ /pi \ \2 csc(2*x) /
/ csc|-- - 2*x|
\/ \2 /
-------------------------------------------
x
$$\frac{\sqrt{\frac{x}{\csc{\left(- 2 x + \frac{\pi}{2} \right)}}} \left(- \frac{x \csc{\left(- 2 x + \frac{\pi}{2} \right)}}{\csc{\left(2 x \right)}} + \frac{1}{2}\right)}{x}$$
/ /pi \ \
_________________ |sin|-- + 2*x| |
/ /pi \ | \2 / |
/ x*sin|-- + 2*x| *|------------- - x*sin(2*x)|
\/ \2 / \ 2 /
--------------------------------------------------
/ 2 \
| sin (2*x)| 2
x*|-1 + ---------|*sin (x)
| 4 |
\ 4*sin (x)/
$$\frac{\sqrt{x \sin{\left(2 x + \frac{\pi}{2} \right)}} \left(- x \sin{\left(2 x \right)} + \frac{\sin{\left(2 x + \frac{\pi}{2} \right)}}{2}\right)}{x \left(-1 + \frac{\sin^{2}{\left(2 x \right)}}{4 \sin^{4}{\left(x \right)}}\right) \sin^{2}{\left(x \right)}}$$
____________ /cos(2*x) \
\/ x*cos(2*x) *|-------- - x*sin(2*x)|
\ 2 /
--------------------------------------
2
/ 2 \ / 2/x\\ 4/x\
x*\1 - tan (x)/*|1 - tan |-|| *cos |-|
\ \2// \2/
$$\frac{\sqrt{x \cos{\left(2 x \right)}} \left(- x \sin{\left(2 x \right)} + \frac{\cos{\left(2 x \right)}}{2}\right)}{x \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{2} \left(1 - \tan^{2}{\left(x \right)}\right) \cos^{4}{\left(\frac{x}{2} \right)}}$$
__________________
/ / 2 \ 2 / 2 \
/ x*\-1 + cot (x)/ / 2/x\\ | -1 + cot (x) 2*x*cot(x)|
/ ---------------- *|1 + cot |-|| *|--------------- - -----------|
/ 2 \ \2// | / 2 \ 2 |
\/ 1 + cot (x) \2*\1 + cot (x)/ 1 + cot (x)/
-----------------------------------------------------------------------
2
/ 1 \ / 2/x\\
x*|1 - -------|*|-1 + cot |-||
| 2 | \ \2//
\ cot (x)/
$$\frac{\sqrt{\frac{x \left(\cot^{2}{\left(x \right)} - 1\right)}{\cot^{2}{\left(x \right)} + 1}} \left(- \frac{2 x \cot{\left(x \right)}}{\cot^{2}{\left(x \right)} + 1} + \frac{\cot^{2}{\left(x \right)} - 1}{2 \left(\cot^{2}{\left(x \right)} + 1\right)}\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}{x \left(1 - \frac{1}{\cot^{2}{\left(x \right)}}\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{2}}$$
_________________
/ / 2 \ 2 / 2 \
/ x*\1 - tan (x)/ / 2/x\\ | 1 - tan (x) 2*x*tan(x)|
/ --------------- *|1 + tan |-|| *|--------------- - -----------|
/ 2 \ \2// | / 2 \ 2 |
\/ 1 + tan (x) \2*\1 + tan (x)/ 1 + tan (x)/
----------------------------------------------------------------------
/ 1 \ 2/x\
4*x*|-1 + -------|*tan |-|
| 2 | \2/
\ tan (x)/
$$\frac{\sqrt{\frac{x \left(1 - \tan^{2}{\left(x \right)}\right)}{\tan^{2}{\left(x \right)} + 1}} \left(- \frac{2 x \tan{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1} + \frac{1 - \tan^{2}{\left(x \right)}}{2 \left(\tan^{2}{\left(x \right)} + 1\right)}\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}{4 x \left(-1 + \frac{1}{\tan^{2}{\left(x \right)}}\right) \tan^{2}{\left(\frac{x}{2} \right)}}$$
sqrt(x*(1 - tan(x)^2)/(1 + tan(x)^2))*(1 + tan(x/2)^2)^2*((1 - tan(x)^2)/(2*(1 + tan(x)^2)) - 2*x*tan(x)/(1 + tan(x)^2))/(4*x*(-1 + tan(x)^(-2))*tan(x/2)^2)
Respuesta numérica
[src]
(x*cos(2*x))^0.5*(0.5*cos(2*x) - x*sin(2*x))/(x*cos(2*x))
(x*cos(2*x))^0.5*(0.5*cos(2*x) - x*sin(2*x))/(x*cos(2*x))