Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
tan(x/2)^4/(2*sqrt(x))+sqrt(x)*tan(x/2)^3*(2+2*tan(x/2)^2)
¿Cómo vas a descomponer esta tan(x/2)^4/(2*sqrt(x))+sqrt(x)*tan(x/2)^3*(2+2*tan(x/2)^2) expresión en fracciones?
Solución
Ha introducido
[src]
4/x\
tan |-|
\2/ ___ 3/x\ / 2/x\\
------- + \/ x *tan |-|*|2 + 2*tan |-||
___ \2/ \ \2//
2*\/ x
$$\sqrt{x} \tan^{3}{\left(\frac{x}{2} \right)} \left(2 \tan^{2}{\left(\frac{x}{2} \right)} + 2\right) + \frac{\tan^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x}}$$
tan(x/2)^4/((2*sqrt(x))) + (sqrt(x)*tan(x/2)^3)*(2 + 2*tan(x/2)^2)
Simplificación general
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3/x\ / 8*x /x\\
tan |-|*|---------- + tan|-||
\2/ \1 + cos(x) \2//
-----------------------------
___
2*\/ x
$$\frac{\left(\frac{8 x}{\cos{\left(x \right)} + 1} + \tan{\left(\frac{x}{2} \right)}\right) \tan^{3}{\left(\frac{x}{2} \right)}}{2 \sqrt{x}}$$
tan(x/2)^3*(8*x/(1 + cos(x)) + tan(x/2))/(2*sqrt(x))
Respuesta numérica
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0.5*x^(-0.5)*tan(x/2)^4 + x^0.5*tan(x/2)^3*(2.0 + 2.0*tan(x/2)^2)
0.5*x^(-0.5)*tan(x/2)^4 + x^0.5*tan(x/2)^3*(2.0 + 2.0*tan(x/2)^2)
Denominador común
[src]
4/x\ 3/x\ 5/x\
tan |-| + 4*x*tan |-| + 4*x*tan |-|
\2/ \2/ \2/
-----------------------------------
___
2*\/ x
$$\frac{4 x \tan^{5}{\left(\frac{x}{2} \right)} + 4 x \tan^{3}{\left(\frac{x}{2} \right)} + \tan^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x}}$$
(tan(x/2)^4 + 4*x*tan(x/2)^3 + 4*x*tan(x/2)^5)/(2*sqrt(x))
Combinatoria
[src]
3/x\ / 2/x\ /x\\
tan |-|*|4*x + 4*x*tan |-| + tan|-||
\2/ \ \2/ \2//
------------------------------------
___
2*\/ x
$$\frac{\left(4 x \tan^{2}{\left(\frac{x}{2} \right)} + 4 x + \tan{\left(\frac{x}{2} \right)}\right) \tan^{3}{\left(\frac{x}{2} \right)}}{2 \sqrt{x}}$$
tan(x/2)^3*(4*x + 4*x*tan(x/2)^2 + tan(x/2))/(2*sqrt(x))
Potencias
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/ 2\
3 | / I*x -I*x \ |
/ I*x -I*x \ | | --- -----| |
| --- -----| | | 2 2 | |
___ | 2 2 | | 2*\- e + e / |
I*\/ x *\- e + e / *|2 - --------------------|
4 | 2 |
/ I*x -I*x \ | / I*x -I*x \ |
| --- -----| | | --- -----| |
| 2 2 | | | 2 2 | |
\- e + e / \ \e + e / /
------------------------ - -----------------------------------------------------
4 3
/ I*x -I*x \ / I*x -I*x \
| --- -----| | --- -----|
___ | 2 2 | | 2 2 |
2*\/ x *\e + e / \e + e /
$$- \frac{i \sqrt{x} \left(- \frac{2 \left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2}}{\left(e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2}} + 2\right) \left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{3}}{\left(e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{3}} + \frac{\left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{4}}{2 \sqrt{x} \left(e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{4}}$$
4/x\
tan |-|
\2/ ___ 3/x\ / 2/x\\
------- + \/ x *tan |-|*|2 + 2*tan |-||
___ \2/ \ \2//
2*\/ x
$$\sqrt{x} \left(2 \tan^{2}{\left(\frac{x}{2} \right)} + 2\right) \tan^{3}{\left(\frac{x}{2} \right)} + \frac{\tan^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x}}$$
tan(x/2)^4/(2*sqrt(x)) + sqrt(x)*tan(x/2)^3*(2 + 2*tan(x/2)^2)
Unión de expresiones racionales
[src]
3/x\ / / 2/x\\ /x\\
tan |-|*|4*x*|1 + tan |-|| + tan|-||
\2/ \ \ \2// \2//
------------------------------------
___
2*\/ x
$$\frac{\left(4 x \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right) + \tan{\left(\frac{x}{2} \right)}\right) \tan^{3}{\left(\frac{x}{2} \right)}}{2 \sqrt{x}}$$
tan(x/2)^3*(4*x*(1 + tan(x/2)^2) + tan(x/2))/(2*sqrt(x))
Parte trigonométrica
[src]
4/x\
tan |-|
\2/ ___ 5/x\ 3/x\
------- + 2*\/ x *sec |-|*sin |-|
___ \2/ \2/
2*\/ x
$$2 \sqrt{x} \sin^{3}{\left(\frac{x}{2} \right)} \sec^{5}{\left(\frac{x}{2} \right)} + \frac{\tan^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x}}$$
___ / 2 \
\/ x *|2 + -------|
| 2/x\|
| cot |-||
1 \ \2//
--------------- + -------------------
___ 4/x\ 3/x\
2*\/ x *cot |-| cot |-|
\2/ \2/
$$\frac{\sqrt{x} \left(2 + \frac{2}{\cot^{2}{\left(\frac{x}{2} \right)}}\right)}{\cot^{3}{\left(\frac{x}{2} \right)}} + \frac{1}{2 \sqrt{x} \cot^{4}{\left(\frac{x}{2} \right)}}$$
2
4/x\ ___ / 2/x\\ 3/x\
tan |-| 16*\/ x *|1 + tan |-|| *tan |-|
\2/ \ \4// \4/
------- + -------------------------------
___ 5
2*\/ x / 2/x\\
|1 - tan |-||
\ \4//
$$\frac{16 \sqrt{x} \left(\tan^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2} \tan^{3}{\left(\frac{x}{4} \right)}}{\left(1 - \tan^{2}{\left(\frac{x}{4} \right)}\right)^{5}} + \frac{\tan^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x}}$$
___
1 4*\/ x
--------------- + --------------------------
___ 4/x\ / 2/x\\
2*\/ x *cot |-| | -1 + cot |-||
\2/ | \2/| 3/x\
|1 + ------------|*cot |-|
| 2/x\ | \2/
| 1 + cot |-| |
\ \2/ /
$$\frac{4 \sqrt{x}}{\left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} + 1\right) \cot^{3}{\left(\frac{x}{2} \right)}} + \frac{1}{2 \sqrt{x} \cot^{4}{\left(\frac{x}{2} \right)}}$$
4/x\ ___ 3/x\
tan |-| 16*\/ x *tan |-|
\2/ \4/
------- + ----------------------
___ 5
2*\/ x / 2/x\\ 4/x\
|1 - tan |-|| *cos |-|
\ \4// \4/
$$\frac{16 \sqrt{x} \tan^{3}{\left(\frac{x}{4} \right)}}{\left(1 - \tan^{2}{\left(\frac{x}{4} \right)}\right)^{5} \cos^{4}{\left(\frac{x}{4} \right)}} + \frac{\tan^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x}}$$
/ 2/x pi\\
| 2*cos |- - --||
___ 3/x pi\ | \2 2 /|
\/ x *cos |- - --|*|2 + --------------|
4/x pi\ \2 2 / | 2/x\ |
cos |- - --| | cos |-| |
\2 2 / \ \2/ /
--------------- + ---------------------------------------
___ 4/x\ 3/x\
2*\/ x *cos |-| cos |-|
\2/ \2/
$$\frac{\sqrt{x} \left(2 + \frac{2 \cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{x}{2} \right)}}\right) \cos^{3}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\cos^{3}{\left(\frac{x}{2} \right)}} + \frac{\cos^{4}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{2 \sqrt{x} \cos^{4}{\left(\frac{x}{2} \right)}}$$
4/pi x\ ___ 5/pi x\
csc |-- - -| 2*\/ x *csc |-- - -|
\2 2/ \2 2/
--------------- + --------------------
___ 4/x\ 3/x\
2*\/ x *csc |-| csc |-|
\2/ \2/
$$\frac{2 \sqrt{x} \csc^{5}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{\csc^{3}{\left(\frac{x}{2} \right)}} + \frac{\csc^{4}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{2 \sqrt{x} \csc^{4}{\left(\frac{x}{2} \right)}}$$
2
___ / 2/x\\
2*\/ x *|1 + cot |-||
1 \ \4//
--------------- + -----------------------
___ 4/x\ 2
2*\/ x *cot |-| / 2/x\\ 3/x\
\2/ |-1 + cot |-|| *cot |-|
\ \4// \2/
$$\frac{2 \sqrt{x} \left(\cot^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2}}{\left(\cot^{2}{\left(\frac{x}{4} \right)} - 1\right)^{2} \cot^{3}{\left(\frac{x}{2} \right)}} + \frac{1}{2 \sqrt{x} \cot^{4}{\left(\frac{x}{2} \right)}}$$
8/x\ ___ 6/x\
8*sin |-| 32*\/ x *sin |-|
\2/ \2/
------------- + -------------------------
___ 4 / / pi\\ 3
\/ x *sin (x) |1 + sin|x + --||*sin (x)
\ \ 2 //
$$\frac{32 \sqrt{x} \sin^{6}{\left(\frac{x}{2} \right)}}{\left(\sin{\left(x + \frac{\pi}{2} \right)} + 1\right) \sin^{3}{\left(x \right)}} + \frac{8 \sin^{8}{\left(\frac{x}{2} \right)}}{\sqrt{x} \sin^{4}{\left(x \right)}}$$
4/x\ ___ 3/x\
tan |-| 2*\/ x *sin |-|
\2/ \2/
------- + ---------------
___ 5/x\
2*\/ x cos |-|
\2/
$$\frac{2 \sqrt{x} \sin^{3}{\left(\frac{x}{2} \right)}}{\cos^{5}{\left(\frac{x}{2} \right)}} + \frac{\tan^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x}}$$
2
4/x\ ___ / 2/x\\ 3/x\
tan |-| 2*\/ x *|1 + tan |-|| *tan |-|
\2/ \ \4// \2/
------- + ------------------------------
___ 2
2*\/ x / 2/x\\
|1 - tan |-||
\ \4//
$$\frac{2 \sqrt{x} \left(\tan^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2} \tan^{3}{\left(\frac{x}{2} \right)}}{\left(1 - \tan^{2}{\left(\frac{x}{4} \right)}\right)^{2}} + \frac{\tan^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x}}$$
4/x pi\ ___ 3/x pi\
cos |- - --| 4*\/ x *cos |- - --|
\2 2 / \2 2 /
--------------- + --------------------
___ 4/x\ 3/x\
2*\/ x *cos |-| (1 + cos(x))*cos |-|
\2/ \2/
$$\frac{4 \sqrt{x} \cos^{3}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\left(\cos{\left(x \right)} + 1\right) \cos^{3}{\left(\frac{x}{2} \right)}} + \frac{\cos^{4}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{2 \sqrt{x} \cos^{4}{\left(\frac{x}{2} \right)}}$$
4/x\ ___ 5/x\
sec |-| 2*\/ x *sec |-|
\2/ \2/
-------------------- + ---------------
___ 4/x pi\ 3/x pi\
2*\/ x *sec |- - --| sec |- - --|
\2 2 / \2 2 /
$$\frac{2 \sqrt{x} \sec^{5}{\left(\frac{x}{2} \right)}}{\sec^{3}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + \frac{\sec^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x} \sec^{4}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}$$
4/x\ ___ 3/x\
tan |-| 2*\/ x *tan |-|
\2/ \2/
------- + ---------------
___ 2/x\
2*\/ x cos |-|
\2/
$$\frac{2 \sqrt{x} \tan^{3}{\left(\frac{x}{2} \right)}}{\cos^{2}{\left(\frac{x}{2} \right)}} + \frac{\tan^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x}}$$
4/x\ ___ 3/x\
tan |-| 4*\/ x *tan |-|
\2/ \2/
------- + ---------------
___ 1 + cos(x)
2*\/ x
$$\frac{4 \sqrt{x} \tan^{3}{\left(\frac{x}{2} \right)}}{\cos{\left(x \right)} + 1} + \frac{\tan^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x}}$$
4/x\ ___ 3/x\
tan |-| 16*\/ x *cot |-|
\2/ \4/
------- + -----------------------
___ 5
2*\/ x / 2/x\\ 4/x\
|-1 + cot |-|| *sin |-|
\ \4// \4/
$$\frac{16 \sqrt{x} \cot^{3}{\left(\frac{x}{4} \right)}}{\left(\cot^{2}{\left(\frac{x}{4} \right)} - 1\right)^{5} \sin^{4}{\left(\frac{x}{4} \right)}} + \frac{\tan^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x}}$$
/ 2/x\\
| 2*sin |-||
___ 3/x\ | \2/|
\/ x *sin |-|*|2 + ---------|
4/x\ \2/ | 2/x\ |
sin |-| | cos |-| |
\2/ \ \2/ /
--------------- + -----------------------------
___ 4/x\ 3/x\
2*\/ x *cos |-| cos |-|
\2/ \2/
$$\frac{\sqrt{x} \left(\frac{2 \sin^{2}{\left(\frac{x}{2} \right)}}{\cos^{2}{\left(\frac{x}{2} \right)}} + 2\right) \sin^{3}{\left(\frac{x}{2} \right)}}{\cos^{3}{\left(\frac{x}{2} \right)}} + \frac{\sin^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x} \cos^{4}{\left(\frac{x}{2} \right)}}$$
2
___ / 2/x\\ 3/x\
16*\/ x *|1 + cot |-|| *cot |-|
1 \ \4// \4/
--------------- + -------------------------------
___ 4/x\ 5
2*\/ x *cot |-| / 2/x\\
\2/ |-1 + cot |-||
\ \4//
$$\frac{16 \sqrt{x} \left(\cot^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2} \cot^{3}{\left(\frac{x}{4} \right)}}{\left(\cot^{2}{\left(\frac{x}{4} \right)} - 1\right)^{5}} + \frac{1}{2 \sqrt{x} \cot^{4}{\left(\frac{x}{2} \right)}}$$
4/x\ ___ 3/x\
sec |-| 4*\/ x *sec |-|
\2/ \2/
-------------------- + -------------------------
___ 4/x pi\ / 1 \ 3/x pi\
2*\/ x *sec |- - --| |1 + ------|*sec |- - --|
\2 2 / \ sec(x)/ \2 2 /
$$\frac{4 \sqrt{x} \sec^{3}{\left(\frac{x}{2} \right)}}{\left(1 + \frac{1}{\sec{\left(x \right)}}\right) \sec^{3}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + \frac{\sec^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x} \sec^{4}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}$$
/ 2/x\ \
| 2*sec |-| |
___ 3/x\ | \2/ |
\/ x *sec |-|*|2 + ------------|
4/x\ \2/ | 2/x pi\|
sec |-| | sec |- - --||
\2/ \ \2 2 //
-------------------- + --------------------------------
___ 4/x pi\ 3/x pi\
2*\/ x *sec |- - --| sec |- - --|
\2 2 / \2 2 /
$$\frac{\sqrt{x} \left(\frac{2 \sec^{2}{\left(\frac{x}{2} \right)}}{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + 2\right) \sec^{3}{\left(\frac{x}{2} \right)}}{\sec^{3}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + \frac{\sec^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x} \sec^{4}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}$$
8/x\ ___ 6/x\
8*sin |-| 16*\/ x *sin |-|
\2/ \2/
------------- + --------------------
___ 4 3 2/pi x\
\/ x *sin (x) sin (x)*sin |-- + -|
\2 2/
$$\frac{16 \sqrt{x} \sin^{6}{\left(\frac{x}{2} \right)}}{\sin^{3}{\left(x \right)} \sin^{2}{\left(\frac{x}{2} + \frac{\pi}{2} \right)}} + \frac{8 \sin^{8}{\left(\frac{x}{2} \right)}}{\sqrt{x} \sin^{4}{\left(x \right)}}$$
/ 4/x\\
| 8*sin |-||
___ 6/x\ | \2/|
8/x\ 8*\/ x *sin |-|*|2 + ---------|
8*sin |-| \2/ | 2 |
\2/ \ sin (x) /
------------- + -------------------------------
___ 4 3
\/ x *sin (x) sin (x)
$$\frac{8 \sqrt{x} \left(\frac{8 \sin^{4}{\left(\frac{x}{2} \right)}}{\sin^{2}{\left(x \right)}} + 2\right) \sin^{6}{\left(\frac{x}{2} \right)}}{\sin^{3}{\left(x \right)}} + \frac{8 \sin^{8}{\left(\frac{x}{2} \right)}}{\sqrt{x} \sin^{4}{\left(x \right)}}$$
___ 3/x\ 8/x\
2*\/ x *sin |-| 8*sin |-|
\2/ \2/
--------------- + -------------
5/pi x\ ___ 4
sin |-- + -| \/ x *sin (x)
\2 2/
$$\frac{2 \sqrt{x} \sin^{3}{\left(\frac{x}{2} \right)}}{\sin^{5}{\left(\frac{x}{2} + \frac{\pi}{2} \right)}} + \frac{8 \sin^{8}{\left(\frac{x}{2} \right)}}{\sqrt{x} \sin^{4}{\left(x \right)}}$$
/ 2/x\\
| 2*sec |-||
___ 3/x\ | \2/|
\/ x *sec |-|*|2 + ---------|
4/x\ \2/ | 2/x\ |
sec |-| | csc |-| |
\2/ \ \2/ /
--------------- + -----------------------------
___ 4/x\ 3/x\
2*\/ x *csc |-| csc |-|
\2/ \2/
$$\frac{\sqrt{x} \left(2 + \frac{2 \sec^{2}{\left(\frac{x}{2} \right)}}{\csc^{2}{\left(\frac{x}{2} \right)}}\right) \sec^{3}{\left(\frac{x}{2} \right)}}{\csc^{3}{\left(\frac{x}{2} \right)}} + \frac{\sec^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x} \csc^{4}{\left(\frac{x}{2} \right)}}$$
4/x\ ___ 3/x\
tan |-| 4*\/ x *tan |-|
\2/ \2/
------- + ---------------
___ 2/x\
2*\/ x 1 - tan |-|
\2/
1 + -----------
2/x\
1 + tan |-|
\2/
$$\frac{4 \sqrt{x} \tan^{3}{\left(\frac{x}{2} \right)}}{\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + 1} + \frac{\tan^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x}}$$
/ 2/pi x\\
| 2*csc |-- - -||
___ 3/pi x\ | \2 2/|
\/ x *csc |-- - -|*|2 + --------------|
4/pi x\ \2 2/ | 2/x\ |
csc |-- - -| | csc |-| |
\2 2/ \ \2/ /
--------------- + ---------------------------------------
___ 4/x\ 3/x\
2*\/ x *csc |-| csc |-|
\2/ \2/
$$\frac{\sqrt{x} \left(2 + \frac{2 \csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{x}{2} \right)}}\right) \csc^{3}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{\csc^{3}{\left(\frac{x}{2} \right)}} + \frac{\csc^{4}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{2 \sqrt{x} \csc^{4}{\left(\frac{x}{2} \right)}}$$
4/x pi\ ___ 3/x pi\
cos |- - --| 2*\/ x *cos |- - --|
\2 2 / \2 2 /
--------------- + --------------------
___ 4/x\ 5/x\
2*\/ x *cos |-| cos |-|
\2/ \2/
$$\frac{2 \sqrt{x} \cos^{3}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\cos^{5}{\left(\frac{x}{2} \right)}} + \frac{\cos^{4}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{2 \sqrt{x} \cos^{4}{\left(\frac{x}{2} \right)}}$$
4/x\ ___ 3/x\
tan |-| 2*\/ x *tan |-|
\2/ \2/
------- + -----------------------
___ 2
2*\/ x / 2/x\\ 4/x\
|-1 + cot |-|| *sin |-|
\ \4// \4/
$$\frac{2 \sqrt{x} \tan^{3}{\left(\frac{x}{2} \right)}}{\left(\cot^{2}{\left(\frac{x}{4} \right)} - 1\right)^{2} \sin^{4}{\left(\frac{x}{4} \right)}} + \frac{\tan^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x}}$$
4/pi x\ ___ 3/pi x\
csc |-- - -| 4*\/ x *csc |-- - -|
\2 2/ \2 2/
--------------- + -------------------------
___ 4/x\ / 1 \ 3/x\
2*\/ x *csc |-| |1 + -----------|*csc |-|
\2/ | /pi \| \2/
| csc|-- - x||
\ \2 //
$$\frac{4 \sqrt{x} \csc^{3}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{\left(1 + \frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right) \csc^{3}{\left(\frac{x}{2} \right)}} + \frac{\csc^{4}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{2 \sqrt{x} \csc^{4}{\left(\frac{x}{2} \right)}}$$
4/x\
tan |-|
\2/ ___ 3/x\ / 2/x\\
------- + \/ x *tan |-|*|2 + 2*tan |-||
___ \2/ \ \2//
2*\/ x
$$\sqrt{x} \left(2 \tan^{2}{\left(\frac{x}{2} \right)} + 2\right) \tan^{3}{\left(\frac{x}{2} \right)} + \frac{\tan^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x}}$$
4/x\ ___ 3/x\
tan |-| 2*\/ x *tan |-|
\2/ \2/
------- + ----------------------
___ 2
2*\/ x / 2/x\\ 4/x\
|1 - tan |-|| *cos |-|
\ \4// \4/
$$\frac{2 \sqrt{x} \tan^{3}{\left(\frac{x}{2} \right)}}{\left(1 - \tan^{2}{\left(\frac{x}{4} \right)}\right)^{2} \cos^{4}{\left(\frac{x}{4} \right)}} + \frac{\tan^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x}}$$
tan(x/2)^4/(2*sqrt(x)) + 2*sqrt(x)*tan(x/2)^3/((1 - tan(x/4)^2)^2*cos(x/4)^4)
Compilar la expresión
[src]
4/x\
tan |-|
\2/ ___ 3/x\ / 2/x\\
------- + \/ x *tan |-|*|2 + 2*tan |-||
___ \2/ \ \2//
2*\/ x
$$\sqrt{x} \left(2 \tan^{2}{\left(\frac{x}{2} \right)} + 2\right) \tan^{3}{\left(\frac{x}{2} \right)} + \frac{\tan^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x}}$$
tan(x/2)^4/(2*sqrt(x)) + sqrt(x)*tan(x/2)^3*(2 + 2*tan(x/2)^2)
Denominador racional
[src]
___ 4/x\ 3/2 3/x\ 3/2 5/x\
\/ x *tan |-| + 4*x *tan |-| + 4*x *tan |-|
\2/ \2/ \2/
-----------------------------------------------
2*x
$$\frac{4 x^{\frac{3}{2}} \tan^{5}{\left(\frac{x}{2} \right)} + 4 x^{\frac{3}{2}} \tan^{3}{\left(\frac{x}{2} \right)} + \sqrt{x} \tan^{4}{\left(\frac{x}{2} \right)}}{2 x}$$
(sqrt(x)*tan(x/2)^4 + 4*x^(3/2)*tan(x/2)^3 + 4*x^(3/2)*tan(x/2)^5)/(2*x)