Descomposición de una fracción
[src]
1/(2*(1 + cot(x^2/2 + pi/3))) + 1/(2*(-1 + cot(x^2/2 + pi/3)))
$$\frac{1}{2 \left(\cot{\left(\frac{x^{2}}{2} + \frac{\pi}{3} \right)} + 1\right)} + \frac{1}{2 \left(\cot{\left(\frac{x^{2}}{2} + \frac{\pi}{3} \right)} - 1\right)}$$
1 1
-------------------- + ---------------------
/ / 2 \\ / / 2 \\
| |x pi|| | |x pi||
2*|1 + cot|-- + --|| 2*|-1 + cot|-- + --||
\ \2 3 // \ \2 3 //
Simplificación general
[src]
/ 2 \
|x pi|
cot|-- + --|
\2 3 /
------------------
1
-1 + -------------
/ 2 \
2|x pi|
tan |-- + --|
\2 3 /
$$\frac{\cot{\left(\frac{x^{2}}{2} + \frac{\pi}{3} \right)}}{-1 + \frac{1}{\tan^{2}{\left(\frac{x^{2}}{2} + \frac{\pi}{3} \right)}}}$$
cot(x^2/2 + pi/3)/(-1 + tan(x^2/2 + pi/3)^(-2))
Denominador racional
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/ 2 2*pi\
|x + ----|
| 3 |
cot|---------|
\ 2 /
------------------
/ 2 \
2|x pi|
-1 + cot |-- + --|
\2 3 /
$$\frac{\cot{\left(\frac{x^{2} + \frac{2 \pi}{3}}{2} \right)}}{\cot^{2}{\left(\frac{x^{2}}{2} + \frac{\pi}{3} \right)} - 1}$$
cot((x^2 + 2*pi/3)/2)/(-1 + cot(x^2/2 + pi/3)^2)
cot(x^2/2 + pi/3)/(-1.0 + cot(x^2/2 + pi/3)^2)
cot(x^2/2 + pi/3)/(-1.0 + cot(x^2/2 + pi/3)^2)
Unión de expresiones racionales
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/ 2\
|2*pi + 3*x |
cot|-----------|
\ 6 /
----------------------
/ 2\
2|2*pi + 3*x |
-1 + cot |-----------|
\ 6 /
$$\frac{\cot{\left(\frac{3 x^{2} + 2 \pi}{6} \right)}}{\cot^{2}{\left(\frac{3 x^{2} + 2 \pi}{6} \right)} - 1}$$
cot((2*pi + 3*x^2)/6)/(-1 + cot((2*pi + 3*x^2)/6)^2)
Abrimos la expresión
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/ 2\
___ |x |
\/ 3 *cot|--|
1 \2 /
- --------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ 2\ / 2\ / 2\ / / 2\ / 2\ / 2\ \
3|x | |x | ___ 2|x | | 3|x | |x | ___ 2|x | |
/ 2\ ___ ___ cot |--| cot|--| 5*\/ 3 *cot |--| | / 2\ ___ ___ cot |--| cot|--| 5*\/ 3 *cot |--| |
|x | \/ 3 \/ 3 \2 / \2 / \2 / | |x | \/ 3 \/ 3 \2 / \2 / \2 / |
- cot|--| - ----- + ---------------------------------- + ---------------------------------- + ---------------------------------- - ---------------------------------- 3*|- cot|--| - ----- + ---------------------------------- + ---------------------------------- + ---------------------------------- - ----------------------------------|
\2 / 3 / / 2\\ / / 2\\ / / 2\\ / / 2\\ | \2 / 3 / / 2\\ / / 2\\ / / 2\\ / / 2\\|
| ___ |x || | ___ |x || | ___ |x || | ___ |x || | | ___ |x || | ___ |x || | ___ |x || | ___ |x |||
| / 2\ 2*\/ 3 *cot|--|| | / 2\ 2*\/ 3 *cot|--|| | / 2\ 2*\/ 3 *cot|--|| | / 2\ 2*\/ 3 *cot|--|| | | / 2\ 2*\/ 3 *cot|--|| | / 2\ 2*\/ 3 *cot|--|| | / 2\ 2*\/ 3 *cot|--|| | / 2\ 2*\/ 3 *cot|--|||
|1 2|x | \2 /| |1 2|x | \2 /| |1 2|x | \2 /| |1 2|x | \2 /| | |1 2|x | \2 /| |1 2|x | \2 /| |1 2|x | \2 /| |1 2|x | \2 /||
3*|- + cot |--| + ---------------| 3*|- + cot |--| + ---------------| 3*|- + cot |--| + ---------------| 9*|- + cot |--| + ---------------| | 3*|- + cot |--| + ---------------| 3*|- + cot |--| + ---------------| 3*|- + cot |--| + ---------------| 9*|- + cot |--| + ---------------||
\3 \2 / 3 / \3 \2 / 3 / \3 \2 / 3 / \3 \2 / 3 / \ \3 \2 / 3 / \3 \2 / 3 / \3 \2 / 3 / \3 \2 / 3 //
$$\frac{\sqrt{3} \cot{\left(\frac{x^{2}}{2} \right)}}{3 \left(- \cot{\left(\frac{x^{2}}{2} \right)} - \frac{\sqrt{3}}{3} + \frac{\cot^{3}{\left(\frac{x^{2}}{2} \right)}}{3 \left(\cot^{2}{\left(\frac{x^{2}}{2} \right)} + \frac{2 \sqrt{3} \cot{\left(\frac{x^{2}}{2} \right)}}{3} + \frac{1}{3}\right)} - \frac{5 \sqrt{3} \cot^{2}{\left(\frac{x^{2}}{2} \right)}}{9 \left(\cot^{2}{\left(\frac{x^{2}}{2} \right)} + \frac{2 \sqrt{3} \cot{\left(\frac{x^{2}}{2} \right)}}{3} + \frac{1}{3}\right)} + \frac{\cot{\left(\frac{x^{2}}{2} \right)}}{3 \left(\cot^{2}{\left(\frac{x^{2}}{2} \right)} + \frac{2 \sqrt{3} \cot{\left(\frac{x^{2}}{2} \right)}}{3} + \frac{1}{3}\right)} + \frac{\sqrt{3}}{3 \left(\cot^{2}{\left(\frac{x^{2}}{2} \right)} + \frac{2 \sqrt{3} \cot{\left(\frac{x^{2}}{2} \right)}}{3} + \frac{1}{3}\right)}\right)} - \frac{1}{- \cot{\left(\frac{x^{2}}{2} \right)} - \frac{\sqrt{3}}{3} + \frac{\cot^{3}{\left(\frac{x^{2}}{2} \right)}}{3 \left(\cot^{2}{\left(\frac{x^{2}}{2} \right)} + \frac{2 \sqrt{3} \cot{\left(\frac{x^{2}}{2} \right)}}{3} + \frac{1}{3}\right)} - \frac{5 \sqrt{3} \cot^{2}{\left(\frac{x^{2}}{2} \right)}}{9 \left(\cot^{2}{\left(\frac{x^{2}}{2} \right)} + \frac{2 \sqrt{3} \cot{\left(\frac{x^{2}}{2} \right)}}{3} + \frac{1}{3}\right)} + \frac{\cot{\left(\frac{x^{2}}{2} \right)}}{3 \left(\cot^{2}{\left(\frac{x^{2}}{2} \right)} + \frac{2 \sqrt{3} \cot{\left(\frac{x^{2}}{2} \right)}}{3} + \frac{1}{3}\right)} + \frac{\sqrt{3}}{3 \left(\cot^{2}{\left(\frac{x^{2}}{2} \right)} + \frac{2 \sqrt{3} \cot{\left(\frac{x^{2}}{2} \right)}}{3} + \frac{1}{3}\right)}}$$
-1/(-cot(x^2/2) - sqrt(3)/3 + sqrt(3)/(3*(1/3 + cot(x^2/2)^2 + 2*sqrt(3)*cot(x^2/2)/3)) + cot(x^2/2)^3/(3*(1/3 + cot(x^2/2)^2 + 2*sqrt(3)*cot(x^2/2)/3)) + cot(x^2/2)/(3*(1/3 + cot(x^2/2)^2 + 2*sqrt(3)*cot(x^2/2)/3)) - 5*sqrt(3)*cot(x^2/2)^2/(9*(1/3 + cot(x^2/2)^2 + 2*sqrt(3)*cot(x^2/2)/3))) + sqrt(3)*cot(x^2/2)/(3*(-cot(x^2/2) - sqrt(3)/3 + sqrt(3)/(3*(1/3 + cot(x^2/2)^2 + 2*sqrt(3)*cot(x^2/2)/3)) + cot(x^2/2)^3/(3*(1/3 + cot(x^2/2)^2 + 2*sqrt(3)*cot(x^2/2)/3)) + cot(x^2/2)/(3*(1/3 + cot(x^2/2)^2 + 2*sqrt(3)*cot(x^2/2)/3)) - 5*sqrt(3)*cot(x^2/2)^2/(9*(1/3 + cot(x^2/2)^2 + 2*sqrt(3)*cot(x^2/2)/3))))
/ 2 \
|x pi|
cot|-- + --|
\2 3 /
--------------------------------------
/ / 2 \\ / / 2 \\
| |x pi|| | |x pi||
|1 + cot|-- + --||*|-1 + cot|-- + --||
\ \2 3 // \ \2 3 //
$$\frac{\cot{\left(\frac{x^{2}}{2} + \frac{\pi}{3} \right)}}{\left(\cot{\left(\frac{x^{2}}{2} + \frac{\pi}{3} \right)} - 1\right) \left(\cot{\left(\frac{x^{2}}{2} + \frac{\pi}{3} \right)} + 1\right)}$$
cot(x^2/2 + pi/3)/((1 + cot(x^2/2 + pi/3))*(-1 + cot(x^2/2 + pi/3)))