Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
log(1+tan(x/2)^2)/(-1+tan(x/2)^2)-log(1+tan(x/2))/(-1+tan(x/2)^2)-log(-1+tan(x/2))/(-1+tan(x/2)^2)+tan(x/2)^2*log(1+tan(x/2))/(-1+tan(x/2)^2)+tan(x/2)^2*log(-1+tan(x/2))/(-1+tan(x/2)^2)-tan(x/2)^2*log(1+tan(x/2)^2)/(-1+tan(x/2)^2)-2*x*tan(x/2)/(-1+tan(x/2)^2)
¿Cómo vas a descomponer esta log(1+tan(x/2)^2)/(-1+tan(x/2)^2)-log(1+tan(x/2))/(-1+tan(x/2)^2)-log(-1+tan(x/2))/(-1+tan(x/2)^2)+tan(x/2)^2*log(1+tan(x/2))/(-1+tan(x/2)^2)+tan(x/2)^2*log(-1+tan(x/2))/(-1+tan(x/2)^2)-tan(x/2)^2*log(1+tan(x/2)^2)/(-1+tan(x/2)^2)-2*x*tan(x/2)/(-1+tan(x/2)^2) expresión en fracciones?
Solución
Ha introducido
[src]
/ 2/x\\ / /x\\ / /x\\ 2/x\ / /x\\ 2/x\ / /x\\ 2/x\ / 2/x\\ /x\
log|1 + tan |-|| log|1 + tan|-|| log|-1 + tan|-|| tan |-|*log|1 + tan|-|| tan |-|*log|-1 + tan|-|| tan |-|*log|1 + tan |-|| 2*x*tan|-|
\ \2// \ \2// \ \2// \2/ \ \2// \2/ \ \2// \2/ \ \2// \2/
---------------- - --------------- - ---------------- + ----------------------- + ------------------------ - ------------------------ - ------------
2/x\ 2/x\ 2/x\ 2/x\ 2/x\ 2/x\ 2/x\
-1 + tan |-| -1 + tan |-| -1 + tan |-| -1 + tan |-| -1 + tan |-| -1 + tan |-| -1 + tan |-|
\2/ \2/ \2/ \2/ \2/ \2/ \2/
$$- \frac{2 x \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1} + \left(- \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1} + \left(\frac{\log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1} + \left(\frac{\log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1} + \left(\left(- \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1} + \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1}\right) - \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1}\right)\right)\right)\right)$$
log(1 + tan(x/2)^2)/(-1 + tan(x/2)^2) - log(1 + tan(x/2))/(-1 + tan(x/2)^2) - log(-1 + tan(x/2))/(-1 + tan(x/2)^2) + (tan(x/2)^2*log(1 + tan(x/2)))/(-1 + tan(x/2)^2) + (tan(x/2)^2*log(-1 + tan(x/2)))/(-1 + tan(x/2)^2) - tan(x/2)^2*log(1 + tan(x/2)^2)/(-1 + tan(x/2)^2) - (2*x)*tan(x/2)/(-1 + tan(x/2)^2)
Simplificación general
[src]
/ /x\\ / /x\\ 2/x\ / /x\\ 2/x\ / /x\\ 2/x\ / 2 \ /x\ / 2 \
- log|1 + tan|-|| - log|-1 + tan|-|| + tan |-|*log|1 + tan|-|| + tan |-|*log|-1 + tan|-|| - tan |-|*log|----------| - 2*x*tan|-| + log|----------|
\ \2// \ \2// \2/ \ \2// \2/ \ \2// \2/ \1 + cos(x)/ \2/ \1 + cos(x)/
--------------------------------------------------------------------------------------------------------------------------------------------------
2/x\
-1 + tan |-|
\2/
$$\frac{- 2 x \tan{\left(\frac{x}{2} \right)} - \log{\left(\frac{2}{\cos{\left(x \right)} + 1} \right)} \tan^{2}{\left(\frac{x}{2} \right)} + \log{\left(\frac{2}{\cos{\left(x \right)} + 1} \right)} + \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)} - \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)} + \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)} - \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1}$$
(-log(1 + tan(x/2)) - log(-1 + tan(x/2)) + tan(x/2)^2*log(1 + tan(x/2)) + tan(x/2)^2*log(-1 + tan(x/2)) - tan(x/2)^2*log(2/(1 + cos(x))) - 2*x*tan(x/2) + log(2/(1 + cos(x))))/(-1 + tan(x/2)^2)
Respuesta numérica
[src]
log(1 + tan(x/2)^2)/(-1.0 + tan(x/2)^2) - log(1 + tan(x/2))/(-1.0 + tan(x/2)^2) - log(-1 + tan(x/2))/(-1.0 + tan(x/2)^2) + tan(x/2)^2*log(1 + tan(x/2))/(-1.0 + tan(x/2)^2) + tan(x/2)^2*log(-1 + tan(x/2))/(-1.0 + tan(x/2)^2) - tan(x/2)^2*log(1 + tan(x/2)^2)/(-1.0 + tan(x/2)^2) - 2.0*x*tan(x/2)/(-1.0 + tan(x/2)^2)
log(1 + tan(x/2)^2)/(-1.0 + tan(x/2)^2) - log(1 + tan(x/2))/(-1.0 + tan(x/2)^2) - log(-1 + tan(x/2))/(-1.0 + tan(x/2)^2) + tan(x/2)^2*log(1 + tan(x/2))/(-1.0 + tan(x/2)^2) + tan(x/2)^2*log(-1 + tan(x/2))/(-1.0 + tan(x/2)^2) - tan(x/2)^2*log(1 + tan(x/2)^2)/(-1.0 + tan(x/2)^2) - 2.0*x*tan(x/2)/(-1.0 + tan(x/2)^2)
Denominador común
[src]
/x\
2*x*tan|-|
/ 2/x\\ \2/ / /x\\ / /x\\
- log|1 + tan |-|| - ------------ + log|1 + tan|-|| + log|-1 + tan|-||
\ \2// 2/x\ \ \2// \ \2//
-1 + tan |-|
\2/
$$- \frac{2 x \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1} + \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)} + \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)} - \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)}$$
-log(1 + tan(x/2)^2) - 2*x*tan(x/2)/(-1 + tan(x/2)^2) + log(1 + tan(x/2)) + log(-1 + tan(x/2))
Denominador racional
[src]
/ /x\\ / /x\\ 2/x\ / /x\\ 2/x\ / /x\\ 2/x\ / 2/x\\ /x\ / 2/x\\
- log|1 + tan|-|| - log|-1 + tan|-|| + tan |-|*log|1 + tan|-|| + tan |-|*log|-1 + tan|-|| - tan |-|*log|1 + tan |-|| - 2*x*tan|-| + log|1 + tan |-||
\ \2// \ \2// \2/ \ \2// \2/ \ \2// \2/ \ \2// \2/ \ \2//
----------------------------------------------------------------------------------------------------------------------------------------------------
2/x\
-1 + tan |-|
\2/
$$\frac{- 2 x \tan{\left(\frac{x}{2} \right)} + \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)} - \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)} + \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)} - \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)} - \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)} + \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1}$$
(-log(1 + tan(x/2)) - log(-1 + tan(x/2)) + tan(x/2)^2*log(1 + tan(x/2)) + tan(x/2)^2*log(-1 + tan(x/2)) - tan(x/2)^2*log(1 + tan(x/2)^2) - 2*x*tan(x/2) + log(1 + tan(x/2)^2))/(-1 + tan(x/2)^2)
Unión de expresiones racionales
[src]
/ /x\\ / /x\\ 2/x\ / /x\\ 2/x\ / /x\\ 2/x\ / 2/x\\ /x\ / 2/x\\
- log|1 + tan|-|| - log|-1 + tan|-|| + tan |-|*log|1 + tan|-|| + tan |-|*log|-1 + tan|-|| - tan |-|*log|1 + tan |-|| - 2*x*tan|-| + log|1 + tan |-||
\ \2// \ \2// \2/ \ \2// \2/ \ \2// \2/ \ \2// \2/ \ \2//
----------------------------------------------------------------------------------------------------------------------------------------------------
2/x\
-1 + tan |-|
\2/
$$\frac{- 2 x \tan{\left(\frac{x}{2} \right)} + \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)} - \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)} + \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)} - \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)} - \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)} + \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1}$$
(-log(1 + tan(x/2)) - log(-1 + tan(x/2)) + tan(x/2)^2*log(1 + tan(x/2)) + tan(x/2)^2*log(-1 + tan(x/2)) - tan(x/2)^2*log(1 + tan(x/2)^2) - 2*x*tan(x/2) + log(1 + tan(x/2)^2))/(-1 + tan(x/2)^2)
Combinatoria
[src]
/ / 2/x\\ 2/x\ / 2/x\\ 2/x\ / /x\\ 2/x\ / /x\\ /x\ / /x\\ / /x\\\
-|- log|1 + tan |-|| + tan |-|*log|1 + tan |-|| - tan |-|*log|1 + tan|-|| - tan |-|*log|-1 + tan|-|| + 2*x*tan|-| + log|1 + tan|-|| + log|-1 + tan|-|||
\ \ \2// \2/ \ \2// \2/ \ \2// \2/ \ \2// \2/ \ \2// \ \2///
--------------------------------------------------------------------------------------------------------------------------------------------------------
/ /x\\ / /x\\
|1 + tan|-||*|-1 + tan|-||
\ \2// \ \2//
$$- \frac{2 x \tan{\left(\frac{x}{2} \right)} - \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)} + \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)} - \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)} + \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)} + \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)} - \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)}}{\left(\tan{\left(\frac{x}{2} \right)} - 1\right) \left(\tan{\left(\frac{x}{2} \right)} + 1\right)}$$
-(-log(1 + tan(x/2)^2) + tan(x/2)^2*log(1 + tan(x/2)^2) - tan(x/2)^2*log(1 + tan(x/2)) - tan(x/2)^2*log(-1 + tan(x/2)) + 2*x*tan(x/2) + log(1 + tan(x/2)) + log(-1 + tan(x/2)))/((1 + tan(x/2))*(-1 + tan(x/2)))
Potencias
[src]
/ 2/x\\ / /x\\ / /x\\ 2/x\ / /x\\ 2/x\ / /x\\ 2/x\ / 2/x\\ /x\
log|1 + tan |-|| log|1 + tan|-|| log|-1 + tan|-|| tan |-|*log|1 + tan|-|| tan |-|*log|-1 + tan|-|| tan |-|*log|1 + tan |-|| 2*x*tan|-|
\ \2// \ \2// \ \2// \2/ \ \2// \2/ \ \2// \2/ \ \2// \2/
---------------- - --------------- - ---------------- + ----------------------- + ------------------------ - ------------------------ - ------------
2/x\ 2/x\ 2/x\ 2/x\ 2/x\ 2/x\ 2/x\
-1 + tan |-| -1 + tan |-| -1 + tan |-| -1 + tan |-| -1 + tan |-| -1 + tan |-| -1 + tan |-|
\2/ \2/ \2/ \2/ \2/ \2/ \2/
$$- \frac{2 x \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1} + \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1} - \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1} + \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1} - \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1} - \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1} + \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1}$$
/ 2\ / 2\
| / I*x -I*x \ | 2 | / I*x -I*x \ |
| | --- -----| | / / I*x -I*x \\ / / I*x -I*x \\ / I*x -I*x \ | | --- -----| | 2 / / I*x -I*x \\ 2 / / I*x -I*x \\
| | 2 2 | | | | --- -----|| | | --- -----|| | --- -----| | | 2 2 | | / I*x -I*x \ | | --- -----|| / I*x -I*x \ | | --- -----||
| \- e + e / | | | 2 2 || | | 2 2 || | 2 2 | | \- e + e / | | --- -----| | | 2 2 || | --- -----| | | 2 2 ||
log|1 - ------------------| | I*\- e + e /| | I*\- e + e /| \- e + e / *log|1 - ------------------| | 2 2 | | I*\- e + e /| | 2 2 | | I*\- e + e /|
| 2 | log|1 + -------------------| log|-1 + -------------------| | 2 | \- e + e / *log|1 + -------------------| \- e + e / *log|-1 + -------------------|
| / I*x -I*x \ | | I*x -I*x | | I*x -I*x | | / I*x -I*x \ | | I*x -I*x | | I*x -I*x | / I*x -I*x \
| | --- -----| | | --- ----- | | --- ----- | | | --- -----| | | --- ----- | | --- ----- | | --- -----|
| | 2 2 | | | 2 2 | | 2 2 | | | 2 2 | | | 2 2 | | 2 2 | | 2 2 |
\ \e + e / / \ e + e / \ e + e / \ \e + e / / \ e + e / \ e + e / 2*I*x*\- e + e /
--------------------------- - ---------------------------- - ----------------------------- + ---------------------------------------------- - ----------------------------------------------- - ------------------------------------------------ - -----------------------------------------
2 2 2 / 2\ / 2\ / 2\ / 2\
/ I*x -I*x \ / I*x -I*x \ / I*x -I*x \ | / I*x -I*x \ | 2 | / I*x -I*x \ | 2 | / I*x -I*x \ | 2 | / I*x -I*x \ |
| --- -----| | --- -----| | --- -----| | | --- -----| | / I*x -I*x \ | | --- -----| | / I*x -I*x \ | | --- -----| | / I*x -I*x \ | | --- -----| | / I*x -I*x \
| 2 2 | | 2 2 | | 2 2 | | | 2 2 | | | --- -----| | | 2 2 | | | --- -----| | | 2 2 | | | --- -----| | | 2 2 | | | --- -----|
\- e + e / \- e + e / \- e + e / | \- e + e / | | 2 2 | | \- e + e / | | 2 2 | | \- e + e / | | 2 2 | | \- e + e / | | 2 2 |
-1 - ------------------ -1 - ------------------ -1 - ------------------ |-1 - ------------------|*\e + e / |-1 - ------------------|*\e + e / |-1 - ------------------|*\e + e / |-1 - ------------------|*\e + e /
2 2 2 | 2 | | 2 | | 2 | | 2 |
/ I*x -I*x \ / I*x -I*x \ / I*x -I*x \ | / I*x -I*x \ | | / I*x -I*x \ | | / I*x -I*x \ | | / I*x -I*x \ |
| --- -----| | --- -----| | --- -----| | | --- -----| | | | --- -----| | | | --- -----| | | | --- -----| |
| 2 2 | | 2 2 | | 2 2 | | | 2 2 | | | | 2 2 | | | | 2 2 | | | | 2 2 | |
\e + e / \e + e / \e + e / \ \e + e / / \ \e + e / / \ \e + e / / \ \e + e / /
$$- \frac{2 i x \left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)}{\left(- \frac{\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}} - 1\right) \left(e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)} + \frac{\left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2} \log{\left(- \frac{\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}} + 1 \right)}}{\left(- \frac{\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}} - 1\right) \left(e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2}} - \frac{\left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2} \log{\left(\frac{i \left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)}{e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}} - 1 \right)}}{\left(- \frac{\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}} - 1\right) \left(e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2}} - \frac{\left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2} \log{\left(\frac{i \left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)}{e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}} + 1 \right)}}{\left(- \frac{\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}} - 1\right) \left(e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2}} + \frac{\log{\left(- \frac{\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}} + 1 \right)}}{- \frac{\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}} - 1} - \frac{\log{\left(\frac{i \left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)}{e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}} - 1 \right)}}{- \frac{\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}} - 1} - \frac{\log{\left(\frac{i \left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)}{e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}} + 1 \right)}}{- \frac{\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}} - 1}$$
log(1 - (-exp(i*x/2) + exp(-i*x/2))^2/(exp(i*x/2) + exp(-i*x/2))^2)/(-1 - (-exp(i*x/2) + exp(-i*x/2))^2/(exp(i*x/2) + exp(-i*x/2))^2) - log(1 + i*(-exp(i*x/2) + exp(-i*x/2))/(exp(i*x/2) + exp(-i*x/2)))/(-1 - (-exp(i*x/2) + exp(-i*x/2))^2/(exp(i*x/2) + exp(-i*x/2))^2) - log(-1 + i*(-exp(i*x/2) + exp(-i*x/2))/(exp(i*x/2) + exp(-i*x/2)))/(-1 - (-exp(i*x/2) + exp(-i*x/2))^2/(exp(i*x/2) + exp(-i*x/2))^2) + (-exp(i*x/2) + exp(-i*x/2))^2*log(1 - (-exp(i*x/2) + exp(-i*x/2))^2/(exp(i*x/2) + exp(-i*x/2))^2)/((-1 - (-exp(i*x/2) + exp(-i*x/2))^2/(exp(i*x/2) + exp(-i*x/2))^2)*(exp(i*x/2) + exp(-i*x/2))^2) - (-exp(i*x/2) + exp(-i*x/2))^2*log(1 + i*(-exp(i*x/2) + exp(-i*x/2))/(exp(i*x/2) + exp(-i*x/2)))/((-1 - (-exp(i*x/2) + exp(-i*x/2))^2/(exp(i*x/2) + exp(-i*x/2))^2)*(exp(i*x/2) + exp(-i*x/2))^2) - (-exp(i*x/2) + exp(-i*x/2))^2*log(-1 + i*(-exp(i*x/2) + exp(-i*x/2))/(exp(i*x/2) + exp(-i*x/2)))/((-1 - (-exp(i*x/2) + exp(-i*x/2))^2/(exp(i*x/2) + exp(-i*x/2))^2)*(exp(i*x/2) + exp(-i*x/2))^2) - 2*i*x*(-exp(i*x/2) + exp(-i*x/2))/((-1 - (-exp(i*x/2) + exp(-i*x/2))^2/(exp(i*x/2) + exp(-i*x/2))^2)*(exp(i*x/2) + exp(-i*x/2)))
Compilar la expresión
[src]
/ 2/x\\ / /x\\ / /x\\ 2/x\ / /x\\ 2/x\ / /x\\ 2/x\ / 2/x\\ /x\
log|1 + tan |-|| log|1 + tan|-|| log|-1 + tan|-|| tan |-|*log|1 + tan|-|| tan |-|*log|-1 + tan|-|| tan |-|*log|1 + tan |-|| 2*x*tan|-|
\ \2// \ \2// \ \2// \2/ \ \2// \2/ \ \2// \2/ \ \2// \2/
---------------- - --------------- - ---------------- + ----------------------- + ------------------------ - ------------------------ - ------------
2/x\ 2/x\ 2/x\ 2/x\ 2/x\ 2/x\ 2/x\
-1 + tan |-| -1 + tan |-| -1 + tan |-| -1 + tan |-| -1 + tan |-| -1 + tan |-| -1 + tan |-|
\2/ \2/ \2/ \2/ \2/ \2/ \2/
$$- \frac{2 x \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1} + \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1} - \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1} + \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1} - \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1} - \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1} + \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1}$$
log(1 + tan(x/2)^2)/(-1 + tan(x/2)^2) - log(1 + tan(x/2))/(-1 + tan(x/2)^2) - log(-1 + tan(x/2))/(-1 + tan(x/2)^2) + tan(x/2)^2*log(1 + tan(x/2))/(-1 + tan(x/2)^2) + tan(x/2)^2*log(-1 + tan(x/2))/(-1 + tan(x/2)^2) - tan(x/2)^2*log(1 + tan(x/2)^2)/(-1 + tan(x/2)^2) - 2*x*tan(x/2)/(-1 + tan(x/2)^2)