Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
cot(acos(x/2)^(1/4))^2*(-3)*(-1-cot(acos(x/2)^(1/4))^2)/((8*sqrt(1-x^2/4)*acos(x/2)^(3/4)))
¿Cómo vas a descomponer esta cot(acos(x/2)^(1/4))^2*(-3)*(-1-cot(acos(x/2)^(1/4))^2)/((8*sqrt(1-x^2/4)*acos(x/2)^(3/4))) expresión en fracciones?
Solución
Ha introducido
[src]
/ _________\ / / _________\\
2| / /x\ | | 2| / /x\ ||
cot |4 / acos|-| |*(-3)*|-1 - cot |4 / acos|-| ||
\\/ \2/ / \ \\/ \2/ //
---------------------------------------------------
________
/ 2
/ x 3/4/x\
8* / 1 - -- *acos |-|
\/ 4 \2/
$$\frac{\left(-3\right) \cot^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)} \left(- \cot^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)} - 1\right)}{8 \sqrt{- \frac{x^{2}}{4} + 1} \operatorname{acos}^{\frac{3}{4}}{\left(\frac{x}{2} \right)}}$$
((cot(acos(x/2)^(1/4))^2*(-3))*(-1 - cot(acos(x/2)^(1/4))^2))/(((8*sqrt(1 - x^2/4))*acos(x/2)^(3/4)))
Simplificación general
[src]
/ _________\
2| / /x\ |
3*cot |4 / acos|-| |
\\/ \2/ /
--------------------------------------------
________ / _________\
/ 2 3/4/x\ 2| / /x\ |
4*\/ 4 - x *acos |-|*sin |4 / acos|-| |
\2/ \\/ \2/ /
$$\frac{3 \cot^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)}}{4 \sqrt{4 - x^{2}} \sin^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)} \operatorname{acos}^{\frac{3}{4}}{\left(\frac{x}{2} \right)}}$$
3*cot(acos(x/2)^(1/4))^2/(4*sqrt(4 - x^2)*acos(x/2)^(3/4)*sin(acos(x/2)^(1/4))^2)
Combinatoria
[src]
/ _________\ / / _________\\
2| / /x\ | | 2| / /x\ ||
3*cot |4 / acos|-| |*|1 + cot |4 / acos|-| ||
\\/ \2/ / \ \\/ \2/ //
-----------------------------------------------
___________________ 3/4/x\
4*\/ -(-2 + x)*(2 + x) *acos |-|
\2/
$$\frac{3 \left(\cot^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)} + 1\right) \cot^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)}}{4 \sqrt{- \left(x - 2\right) \left(x + 2\right)} \operatorname{acos}^{\frac{3}{4}}{\left(\frac{x}{2} \right)}}$$
3*cot(acos(x/2)^(1/4))^2*(1 + cot(acos(x/2)^(1/4))^2)/(4*sqrt(-(-2 + x)*(2 + x))*acos(x/2)^(3/4))
Respuesta numérica
[src]
-0.375*(1.0 - 0.25*x^2)^(-0.5)*acos(x/2)^(-0.75)*cot(acos(x/2)^(1/4))^2*(-1.0 - cot(acos(x/2)^(1/4))^2)
-0.375*(1.0 - 0.25*x^2)^(-0.5)*acos(x/2)^(-0.75)*cot(acos(x/2)^(1/4))^2*(-1.0 - cot(acos(x/2)^(1/4))^2)
Denominador racional
[src]
________ / _________\ ________ / _________\
/ 2 2| / /x\ | / 2 4| / /x\ |
- 3*\/ 4 - x *cot |4 / acos|-| | - 3*\/ 4 - x *cot |4 / acos|-| |
\\/ \2/ / \\/ \2/ /
-----------------------------------------------------------------------
/ 2\ 3/4/x\
4*\-4 + x /*acos |-|
\2/
$$\frac{- 3 \sqrt{4 - x^{2}} \cot^{4}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)} - 3 \sqrt{4 - x^{2}} \cot^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)}}{4 \left(x^{2} - 4\right) \operatorname{acos}^{\frac{3}{4}}{\left(\frac{x}{2} \right)}}$$
(-3*sqrt(4 - x^2)*cot(acos(x/2)^(1/4))^2 - 3*sqrt(4 - x^2)*cot(acos(x/2)^(1/4))^4)/(4*(-4 + x^2)*acos(x/2)^(3/4))
Potencias
[src]
/ / _________\\
| 2| / /x\ ||
/ _________\ | 3*cot |4 / acos|-| ||
2| / /x\ | |3 \\/ \2/ /|
cot |4 / acos|-| |*|- + ---------------------|
\\/ \2/ / \8 8 /
-----------------------------------------------
________
/ 2
/ x 3/4/x\
/ 1 - -- *acos |-|
\/ 4 \2/
$$\frac{\left(\frac{3 \cot^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)}}{8} + \frac{3}{8}\right) \cot^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)}}{\sqrt{1 - \frac{x^{2}}{4}} \operatorname{acos}^{\frac{3}{4}}{\left(\frac{x}{2} \right)}}$$
/ _________\ / / _________\\
2| / /x\ | | 2| / /x\ ||
-3*cot |4 / acos|-| |*|-1 - cot |4 / acos|-| ||
\\/ \2/ / \ \\/ \2/ //
-------------------------------------------------
________
/ 2
/ x 3/4/x\
8* / 1 - -- *acos |-|
\/ 4 \2/
$$- \frac{3 \left(- \cot^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)} - 1\right) \cot^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)}}{8 \sqrt{1 - \frac{x^{2}}{4}} \operatorname{acos}^{\frac{3}{4}}{\left(\frac{x}{2} \right)}}$$
-3*cot(acos(x/2)^(1/4))^2*(-1 - cot(acos(x/2)^(1/4))^2)/(8*sqrt(1 - x^2/4)*acos(x/2)^(3/4))
Denominador común
[src]
/ _________\ / _________\
2| / /x\ | 4| / /x\ |
3*cot |4 / acos|-| | + 3*cot |4 / acos|-| |
\\/ \2/ / \\/ \2/ /
---------------------------------------------
________
/ 2 3/4/x\
4*\/ 4 - x *acos |-|
\2/
$$\frac{3 \cot^{4}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)} + 3 \cot^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)}}{4 \sqrt{4 - x^{2}} \operatorname{acos}^{\frac{3}{4}}{\left(\frac{x}{2} \right)}}$$
(3*cot(acos(x/2)^(1/4))^2 + 3*cot(acos(x/2)^(1/4))^4)/(4*sqrt(4 - x^2)*acos(x/2)^(3/4))
Compilar la expresión
[src]
/ _________\ / / _________\\
2| / /x\ | | 2| / /x\ ||
-3*cot |4 / acos|-| |*|-1 - cot |4 / acos|-| ||
\\/ \2/ / \ \\/ \2/ //
-------------------------------------------------
________
/ 2
/ x 3/4/x\
8* / 1 - -- *acos |-|
\/ 4 \2/
$$- \frac{3 \left(- \cot^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)} - 1\right) \cot^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)}}{8 \sqrt{1 - \frac{x^{2}}{4}} \operatorname{acos}^{\frac{3}{4}}{\left(\frac{x}{2} \right)}}$$
-3*cot(acos(x/2)^(1/4))^2*(-1 - cot(acos(x/2)^(1/4))^2)/(8*sqrt(1 - x^2/4)*acos(x/2)^(3/4))
Parte trigonométrica
[src]
/ _________\
2| / /x\ |
3*cot |4 / acos|-| |
\\/ \2/ /
----------------------------------------------
________
/ 2 / _________\
/ x 3/4/x\ 2| / /x\ |
8* / 1 - -- *acos |-|*sin |4 / acos|-| |
\/ 4 \2/ \\/ \2/ /
$$\frac{3 \cot^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)}}{8 \sqrt{1 - \frac{x^{2}}{4}} \sin^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)} \operatorname{acos}^{\frac{3}{4}}{\left(\frac{x}{2} \right)}}$$
/ _________\ / _________\
2| / /x\ | 4| / /x\ |
3*cos |4 / acos|-| |*csc |4 / acos|-| |
\\/ \2/ / \\/ \2/ /
-----------------------------------------
________
/ 2
/ x 3/4/x\
8* / 1 - -- *acos |-|
\/ 4 \2/
$$\frac{3 \cos^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)} \csc^{4}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)}}{8 \sqrt{1 - \frac{x^{2}}{4}} \operatorname{acos}^{\frac{3}{4}}{\left(\frac{x}{2} \right)}}$$
2 2
/ / _________\\ / / _________\\
| | / /x\ || | | / /x\ ||
| |4 / acos|-| || | |4 / acos|-| ||
| 2|\/ \2/ || | 2|\/ \2/ ||
3*|1 + cot |-------------|| *|-1 + cot |-------------||
\ \ 2 // \ \ 2 //
--------------------------------------------------------
/ _________\
________ | / /x\ |
/ 2 |4 / acos|-| |
/ x 3/4/x\ 4|\/ \2/ |
128* / 1 - -- *acos |-|*cot |-------------|
\/ 4 \2/ \ 2 /
$$\frac{3 \left(\cot^{2}{\left(\frac{\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}}}{2} \right)} - 1\right)^{2} \left(\cot^{2}{\left(\frac{\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}}}{2} \right)} + 1\right)^{2}}{128 \sqrt{1 - \frac{x^{2}}{4}} \cot^{4}{\left(\frac{\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}}}{2} \right)} \operatorname{acos}^{\frac{3}{4}}{\left(\frac{x}{2} \right)}}$$
2
/ / _________\\
| | / /x\ ||
| |4 / acos|-| || / _________\
| 2|\/ \2/ || 2| / /x\ |
3*|1 + cot |-------------|| *cot |4 / acos|-| |
\ \ 2 // \\/ \2/ /
------------------------------------------------
/ _________\
________ | / /x\ |
/ 2 |4 / acos|-| |
/ x 3/4/x\ 2|\/ \2/ |
32* / 1 - -- *acos |-|*cot |-------------|
\/ 4 \2/ \ 2 /
$$\frac{3 \left(\cot^{2}{\left(\frac{\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}}}{2} \right)} + 1\right)^{2} \cot^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)}}{32 \sqrt{1 - \frac{x^{2}}{4}} \cot^{2}{\left(\frac{\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}}}{2} \right)} \operatorname{acos}^{\frac{3}{4}}{\left(\frac{x}{2} \right)}}$$
/ / _________\ \
| 2| / /x\ | |
/ _________\ | cos |4 / acos|-| | |
2| / /x\ | | \\/ \2/ / |
-3*cos |4 / acos|-| |*|-1 - ------------------------|
\\/ \2/ / | / _________ \|
| 2| / /x\ pi||
| cos |4 / acos|-| - --||
\ \\/ \2/ 2 //
------------------------------------------------------
________
/ 2 / _________ \
/ x 3/4/x\ 2| / /x\ pi|
8* / 1 - -- *acos |-|*cos |4 / acos|-| - --|
\/ 4 \2/ \\/ \2/ 2 /
$$- \frac{3 \left(-1 - \frac{\cos^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)}}{\cos^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} - \frac{\pi}{2} \right)}}\right) \cos^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)}}{8 \sqrt{1 - \frac{x^{2}}{4}} \cos^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} - \frac{\pi}{2} \right)} \operatorname{acos}^{\frac{3}{4}}{\left(\frac{x}{2} \right)}}$$
/ 1 \
-3*|-1 - -------------------|
| / _________\|
| 2| / /x\ ||
| tan |4 / acos|-| ||
\ \\/ \2/ //
----------------------------------------------
________
/ 2 / _________\
/ x 3/4/x\ 2| / /x\ |
8* / 1 - -- *acos |-|*tan |4 / acos|-| |
\/ 4 \2/ \\/ \2/ /
$$- \frac{3 \left(-1 - \frac{1}{\tan^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)}}\right)}{8 \sqrt{1 - \frac{x^{2}}{4}} \tan^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)} \operatorname{acos}^{\frac{3}{4}}{\left(\frac{x}{2} \right)}}$$
2
/ / _________\\
| | / /x\ ||
| |4 / acos|-| ||
| 2|\/ \2/ ||
3*|1 - tan |-------------||
\ \ 2 //
--------------------------------------------------------------------
/ _________\ / _________\
________ | / /x\ | | / /x\ |
/ 2 |4 / acos|-| | |4 / acos|-| |
/ x 3/4/x\ 4|\/ \2/ | 4|\/ \2/ |
128* / 1 - -- *acos |-|*cos |-------------|*tan |-------------|
\/ 4 \2/ \ 2 / \ 2 /
$$\frac{3 \left(1 - \tan^{2}{\left(\frac{\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}}}{2} \right)}\right)^{2}}{128 \sqrt{1 - \frac{x^{2}}{4}} \cos^{4}{\left(\frac{\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}}}{2} \right)} \tan^{4}{\left(\frac{\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}}}{2} \right)} \operatorname{acos}^{\frac{3}{4}}{\left(\frac{x}{2} \right)}}$$
/ _________\
2| / /x\ |
3*cos |4 / acos|-| |
\\/ \2/ /
----------------------------------------------
________
/ 2 / _________\
/ x 3/4/x\ 4| / /x\ |
8* / 1 - -- *acos |-|*sin |4 / acos|-| |
\/ 4 \2/ \\/ \2/ /
$$\frac{3 \cos^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)}}{8 \sqrt{1 - \frac{x^{2}}{4}} \sin^{4}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)} \operatorname{acos}^{\frac{3}{4}}{\left(\frac{x}{2} \right)}}$$
/ / _________\ \
| 2| / /x\ | |
/ _________\ | csc |4 / acos|-| | |
2| / /x\ | | \\/ \2/ / |
-3*csc |4 / acos|-| |*|-1 - ------------------------|
\\/ \2/ / | / _________\|
| 2|pi / /x\ ||
| csc |-- - 4 / acos|-| ||
\ \2 \/ \2/ //
------------------------------------------------------
________
/ 2 / _________\
/ x 3/4/x\ 2|pi / /x\ |
8* / 1 - -- *acos |-|*csc |-- - 4 / acos|-| |
\/ 4 \2/ \2 \/ \2/ /
$$- \frac{3 \left(-1 - \frac{\csc^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)}}{\csc^{2}{\left(- \sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} + \frac{\pi}{2} \right)}}\right) \csc^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)}}{8 \sqrt{1 - \frac{x^{2}}{4}} \operatorname{acos}^{\frac{3}{4}}{\left(\frac{x}{2} \right)} \csc^{2}{\left(- \sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} + \frac{\pi}{2} \right)}}$$
2
/ / _________\\
| | / /x\ ||
| |4 / acos|-| ||
| 2|\/ \2/ ||
3*|1 + tan |-------------||
\ \ 2 //
-------------------------------------------------------------------
/ _________\
________ | / /x\ |
/ 2 / _________\ |4 / acos|-| |
/ x 3/4/x\ 2| / /x\ | 2|\/ \2/ |
32* / 1 - -- *acos |-|*tan |4 / acos|-| |*tan |-------------|
\/ 4 \2/ \\/ \2/ / \ 2 /
$$\frac{3 \left(\tan^{2}{\left(\frac{\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}}}{2} \right)} + 1\right)^{2}}{32 \sqrt{1 - \frac{x^{2}}{4}} \tan^{2}{\left(\frac{\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}}}{2} \right)} \tan^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)} \operatorname{acos}^{\frac{3}{4}}{\left(\frac{x}{2} \right)}}$$
2
/ / _________\\ / _________\
| | / /x\ || | / /x\ |
| |4 / acos|-| || |4 / acos|-| |
| 2|\/ \2/ || 4|\/ \2/ |
3*|-1 + cot |-------------|| *tan |-------------|
\ \ 2 // \ 2 /
-------------------------------------------------
/ _________\
________ | / /x\ |
/ 2 |4 / acos|-| |
/ x 3/4/x\ 4|\/ \2/ |
128* / 1 - -- *acos |-|*sin |-------------|
\/ 4 \2/ \ 2 /
$$\frac{3 \left(\cot^{2}{\left(\frac{\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}}}{2} \right)} - 1\right)^{2} \tan^{4}{\left(\frac{\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}}}{2} \right)}}{128 \sqrt{1 - \frac{x^{2}}{4}} \sin^{4}{\left(\frac{\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}}}{2} \right)} \operatorname{acos}^{\frac{3}{4}}{\left(\frac{x}{2} \right)}}$$
2 2
/ / _________\\ / / _________\\
| | / /x\ || | | / /x\ ||
| |4 / acos|-| || | |4 / acos|-| ||
| 2|\/ \2/ || | 2|\/ \2/ ||
3*|1 + tan |-------------|| *|1 - tan |-------------||
\ \ 2 // \ \ 2 //
-------------------------------------------------------
/ _________\
________ | / /x\ |
/ 2 |4 / acos|-| |
/ x 3/4/x\ 4|\/ \2/ |
128* / 1 - -- *acos |-|*tan |-------------|
\/ 4 \2/ \ 2 /
$$\frac{3 \left(1 - \tan^{2}{\left(\frac{\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}}}{2} \right)}\right)^{2} \left(\tan^{2}{\left(\frac{\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}}}{2} \right)} + 1\right)^{2}}{128 \sqrt{1 - \frac{x^{2}}{4}} \tan^{4}{\left(\frac{\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}}}{2} \right)} \operatorname{acos}^{\frac{3}{4}}{\left(\frac{x}{2} \right)}}$$
/ _________\
2| / /x\ |
3*cos |4 / acos|-| |
\\/ \2/ /
---------------------------------------------------
________
/ 2 / _________ \
/ x 3/4/x\ 4| / /x\ pi|
8* / 1 - -- *acos |-|*cos |4 / acos|-| - --|
\/ 4 \2/ \\/ \2/ 2 /
$$\frac{3 \cos^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)}}{8 \sqrt{1 - \frac{x^{2}}{4}} \cos^{4}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} - \frac{\pi}{2} \right)} \operatorname{acos}^{\frac{3}{4}}{\left(\frac{x}{2} \right)}}$$
/ / _________\\
| 2| / /x\ ||
/ _________\ | sin |2*4 / acos|-| ||
2| / /x\ | | \ \/ \2/ /|
-3*sin |2*4 / acos|-| |*|-1 - ---------------------|
\ \/ \2/ / | / _________\|
| 4| / /x\ ||
| 4*sin |4 / acos|-| ||
\ \\/ \2/ //
-----------------------------------------------------
________
/ 2 / _________\
/ x 3/4/x\ 4| / /x\ |
32* / 1 - -- *acos |-|*sin |4 / acos|-| |
\/ 4 \2/ \\/ \2/ /
$$- \frac{3 \left(-1 - \frac{\sin^{2}{\left(2 \sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)}}{4 \sin^{4}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)}}\right) \sin^{2}{\left(2 \sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)}}{32 \sqrt{1 - \frac{x^{2}}{4}} \sin^{4}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)} \operatorname{acos}^{\frac{3}{4}}{\left(\frac{x}{2} \right)}}$$
/ _________\ / / _________\\
2| / /x\ | | 2| / /x\ ||
-3*cot |4 / acos|-| |*|-1 - cot |4 / acos|-| ||
\\/ \2/ / \ \\/ \2/ //
-------------------------------------------------
________
/ 2
/ x 3/4/x\
8* / 1 - -- *acos |-|
\/ 4 \2/
$$- \frac{3 \left(- \cot^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)} - 1\right) \cot^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)}}{8 \sqrt{1 - \frac{x^{2}}{4}} \operatorname{acos}^{\frac{3}{4}}{\left(\frac{x}{2} \right)}}$$
/ _________ \
4| / /x\ pi|
3*sec |4 / acos|-| - --|
\\/ \2/ 2 /
----------------------------------------------
________
/ 2 / _________\
/ x 3/4/x\ 2| / /x\ |
8* / 1 - -- *acos |-|*sec |4 / acos|-| |
\/ 4 \2/ \\/ \2/ /
$$\frac{3 \sec^{4}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} - \frac{\pi}{2} \right)}}{8 \sqrt{1 - \frac{x^{2}}{4}} \operatorname{acos}^{\frac{3}{4}}{\left(\frac{x}{2} \right)} \sec^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)}}$$
/ _________ \
2| / /x\ pi|
3*sin |4 / acos|-| + --|
\\/ \2/ 2 /
----------------------------------------------
________
/ 2 / _________\
/ x 3/4/x\ 4| / /x\ |
8* / 1 - -- *acos |-|*sin |4 / acos|-| |
\/ 4 \2/ \\/ \2/ /
$$\frac{3 \sin^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} + \frac{\pi}{2} \right)}}{8 \sqrt{1 - \frac{x^{2}}{4}} \sin^{4}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)} \operatorname{acos}^{\frac{3}{4}}{\left(\frac{x}{2} \right)}}$$
/ / _________ \\
| 2| / /x\ pi||
/ _________ \ | sec |4 / acos|-| - --||
2| / /x\ pi| | \\/ \2/ 2 /|
-3*sec |4 / acos|-| - --|*|-1 - ------------------------|
\\/ \2/ 2 / | / _________\ |
| 2| / /x\ | |
| sec |4 / acos|-| | |
\ \\/ \2/ / /
-----------------------------------------------------------
________
/ 2 / _________\
/ x 3/4/x\ 2| / /x\ |
8* / 1 - -- *acos |-|*sec |4 / acos|-| |
\/ 4 \2/ \\/ \2/ /
$$- \frac{3 \left(- \frac{\sec^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)}} - 1\right) \sec^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} - \frac{\pi}{2} \right)}}{8 \sqrt{1 - \frac{x^{2}}{4}} \operatorname{acos}^{\frac{3}{4}}{\left(\frac{x}{2} \right)} \sec^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)}}$$
3
-------------------------------------------------------------------------
________
/ / _________\\ / 2 / _________\
| | / /x\ || / x 3/4/x\ 2| / /x\ |
4*|1 - cos|2*4 / acos|-| ||* / 1 - -- *acos |-|*tan |4 / acos|-| |
\ \ \/ \2/ // \/ 4 \2/ \\/ \2/ /
$$\frac{3}{4 \sqrt{1 - \frac{x^{2}}{4}} \left(1 - \cos{\left(2 \sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)}\right) \tan^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)} \operatorname{acos}^{\frac{3}{4}}{\left(\frac{x}{2} \right)}}$$
/ _________\
2| / /x\ |
3*cos |4 / acos|-| |
\\/ \2/ /
----------------------------------------------
________
/ 2 / _________\
/ x 3/4/x\ 4| / /x\ |
8* / 1 - -- *acos |-|*sin |4 / acos|-| |
\/ 4 \2/ \\/ \2/ /
$$\frac{3 \cos^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)}}{8 \sqrt{- \frac{x^{2}}{4} + 1} \sin^{4}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)} \operatorname{acos}^{\frac{3}{4}}{\left(\frac{x}{2} \right)}}$$
/ _________\
4| / /x\ |
3*csc |4 / acos|-| |
\\/ \2/ /
---------------------------------------------------
________
/ 2 / _________\
/ x 3/4/x\ 2|pi / /x\ |
8* / 1 - -- *acos |-|*csc |-- - 4 / acos|-| |
\/ 4 \2/ \2 \/ \2/ /
$$\frac{3 \csc^{4}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)}}{8 \sqrt{1 - \frac{x^{2}}{4}} \operatorname{acos}^{\frac{3}{4}}{\left(\frac{x}{2} \right)} \csc^{2}{\left(- \sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} + \frac{\pi}{2} \right)}}$$
/ _________\
2| / /x\ |
3*sin |2*4 / acos|-| |
\ \/ \2/ /
-----------------------------------------------
________
/ 2 / _________\
/ x 3/4/x\ 6| / /x\ |
32* / 1 - -- *acos |-|*sin |4 / acos|-| |
\/ 4 \2/ \\/ \2/ /
$$\frac{3 \sin^{2}{\left(2 \sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)}}{32 \sqrt{1 - \frac{x^{2}}{4}} \sin^{6}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)} \operatorname{acos}^{\frac{3}{4}}{\left(\frac{x}{2} \right)}}$$
/ / _________\\
| 2| / /x\ ||
/ _________\ | csc |4 / acos|-| ||
2| / /x\ | | \\/ \2/ /|
-3*csc |4 / acos|-| |*|-1 - -------------------|
\\/ \2/ / | / _________\|
| 2| / /x\ ||
| sec |4 / acos|-| ||
\ \\/ \2/ //
-------------------------------------------------
________
/ 2 / _________\
/ x 3/4/x\ 2| / /x\ |
8* / 1 - -- *acos |-|*sec |4 / acos|-| |
\/ 4 \2/ \\/ \2/ /
$$- \frac{3 \left(- \frac{\csc^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)}}{\sec^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)}} - 1\right) \csc^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)}}{8 \sqrt{1 - \frac{x^{2}}{4}} \operatorname{acos}^{\frac{3}{4}}{\left(\frac{x}{2} \right)} \sec^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)}}$$
/ / _________\\
| 2| / /x\ ||
/ _________\ | cos |4 / acos|-| ||
2| / /x\ | | \\/ \2/ /|
-3*cos |4 / acos|-| |*|-1 - -------------------|
\\/ \2/ / | / _________\|
| 2| / /x\ ||
| sin |4 / acos|-| ||
\ \\/ \2/ //
-------------------------------------------------
________
/ 2 / _________\
/ x 3/4/x\ 2| / /x\ |
8* / 1 - -- *acos |-|*sin |4 / acos|-| |
\/ 4 \2/ \\/ \2/ /
$$- \frac{3 \left(-1 - \frac{\cos^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)}}{\sin^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)}}\right) \cos^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)}}{8 \sqrt{1 - \frac{x^{2}}{4}} \sin^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)} \operatorname{acos}^{\frac{3}{4}}{\left(\frac{x}{2} \right)}}$$
-3*cos(acos(x/2)^(1/4))^2*(-1 - cos(acos(x/2)^(1/4))^2/sin(acos(x/2)^(1/4))^2)/(8*sqrt(1 - x^2/4)*acos(x/2)^(3/4)*sin(acos(x/2)^(1/4))^2)
Unión de expresiones racionales
[src]
/ _________\ / / _________\\
2| / /x\ | | 2| / /x\ ||
-3*cot |4 / acos|-| |*|-1 - cot |4 / acos|-| ||
\\/ \2/ / \ \\/ \2/ //
-------------------------------------------------
________
/ 2 3/4/x\
4*\/ 4 - x *acos |-|
\2/
$$- \frac{3 \left(- \cot^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)} - 1\right) \cot^{2}{\left(\sqrt[4]{\operatorname{acos}{\left(\frac{x}{2} \right)}} \right)}}{4 \sqrt{4 - x^{2}} \operatorname{acos}^{\frac{3}{4}}{\left(\frac{x}{2} \right)}}$$
-3*cot(acos(x/2)^(1/4))^2*(-1 - cot(acos(x/2)^(1/4))^2)/(4*sqrt(4 - x^2)*acos(x/2)^(3/4))