Sr Examen

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Simplificación de expresiones/ Descomposición en fracciones simples/ tan(t)^atan(t)*((log(tan(t))/(1+t^2)+(1+tan(t)^2)*atan(t)/tan(t))^2+2*(1+tan(t)^2)*atan(t)-(1+tan(t)^2)^2*atan(t)/tan(t)^2-2*t*log(tan(t))/(1+t^2)^2+2*(1+tan(t)^2)/((1+t^2)*tan(t)))

¿Cómo vas a descomponer esta tan(t)^atan(t)*((log(tan(t))/(1+t^2)+(1+tan(t)^2)*atan(t)/tan(t))^2+2*(1+tan(t)^2)*atan(t)-(1+tan(t)^2)^2*atan(t)/tan(t)^2-2*t*log(tan(t))/(1+t^2)^2+2*(1+tan(t)^2)/((1+t^2)*tan(t))) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
              /                                     2                                          2                                            \
              |/              /       2   \        \                              /       2   \                                /       2   \|
   atan(t)    ||log(tan(t))   \1 + tan (t)/*atan(t)|      /       2   \           \1 + tan (t)/ *atan(t)   2*t*log(tan(t))   2*\1 + tan (t)/|
tan       (t)*||----------- + ---------------------|  + 2*\1 + tan (t)/*atan(t) - ---------------------- - --------------- + ---------------|
              ||        2             tan(t)       |                                        2                         2      /     2\       |
              |\   1 + t                           /                                     tan (t)              /     2\       \1 + t /*tan(t)|
              \                                                                                               \1 + t /                      /
((−2tlog⁡(tan⁡(t))(t2+1)2+(−(tan⁡2(t)+1)2atan⁡(t)tan⁡2(t)+(((tan⁡2(t)+1)atan⁡(t)tan⁡(t)+log⁡(tan⁡(t))t2+1)2+2(tan⁡2(t)+1)atan⁡(t))))+2(tan⁡2(t)+1)(t2+1)tan⁡(t))tan⁡atan⁡(t)(t)\left(\left(- \frac{2 t \log{\left(\tan{\left(t \right)} \right)}}{\left(t^{2} + 1\right)^{2}} + \left(- \frac{\left(\tan^{2}{\left(t \right)} + 1\right)^{2} \operatorname{atan}{\left(t \right)}}{\tan^{2}{\left(t \right)}} + \left(\left(\frac{\left(\tan^{2}{\left(t \right)} + 1\right) \operatorname{atan}{\left(t \right)}}{\tan{\left(t \right)}} + \frac{\log{\left(\tan{\left(t \right)} \right)}}{t^{2} + 1}\right)^{2} + 2 \left(\tan^{2}{\left(t \right)} + 1\right) \operatorname{atan}{\left(t \right)}\right)\right)\right) + \frac{2 \left(\tan^{2}{\left(t \right)} + 1\right)}{\left(t^{2} + 1\right) \tan{\left(t \right)}}\right) \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} 
tan(t)^atan(t)*((log(tan(t))/(1 + t^2) + ((1 + tan(t)^2)*atan(t))/tan(t))^2 + (2*(1 + tan(t)^2))*atan(t) - (1 + tan(t)^2)^2*atan(t)/tan(t)^2 - (2*t)*log(tan(t))/(1 + t^2)^2 + (2*(1 + tan(t)^2))/(((1 + t^2)*tan(t))))
Simplificación general [src] 
                   /                                       2                               2                                               2                \
                   |/                     /     2\        \    /       2\          /     2\                                        /     2\     2           |
   -2 + atan(t)    ||                     \1 + t /*atan(t)|    \2 + 2*t /*tan(t)   \1 + t / *atan(t)          2                  2*\1 + t / *tan (t)*atan(t)|
tan            (t)*||log(tan(t))*tan(t) + ----------------|  + ----------------- - ----------------- - 2*t*tan (t)*log(tan(t)) + ---------------------------|
                   ||                            2        |            2                   4                                                  2             |
                   \\                         cos (t)     /         cos (t)             cos (t)                                            cos (t)          /
-------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                  2                                                                          
                                                                          /     2\                                                                           
                                                                          \1 + t /
(−2tlog⁡(tan⁡(t))tan⁡2(t)+2(t2+1)2tan⁡2(t)atan⁡(t)cos⁡2(t)−(t2+1)2atan⁡(t)cos⁡4(t)+(2t2+2)tan⁡(t)cos⁡2(t)+((t2+1)atan⁡(t)cos⁡2(t)+log⁡(tan⁡(t))tan⁡(t))2)tan⁡atan⁡(t)−2(t)(t2+1)2\frac{\left(- 2 t \log{\left(\tan{\left(t \right)} \right)} \tan^{2}{\left(t \right)} + \frac{2 \left(t^{2} + 1\right)^{2} \tan^{2}{\left(t \right)} \operatorname{atan}{\left(t \right)}}{\cos^{2}{\left(t \right)}} - \frac{\left(t^{2} + 1\right)^{2} \operatorname{atan}{\left(t \right)}}{\cos^{4}{\left(t \right)}} + \frac{\left(2 t^{2} + 2\right) \tan{\left(t \right)}}{\cos^{2}{\left(t \right)}} + \left(\frac{\left(t^{2} + 1\right) \operatorname{atan}{\left(t \right)}}{\cos^{2}{\left(t \right)}} + \log{\left(\tan{\left(t \right)} \right)} \tan{\left(t \right)}\right)^{2}\right) \tan^{\operatorname{atan}{\left(t \right)} - 2}{\left(t \right)}}{\left(t^{2} + 1\right)^{2}} 
tan(t)^(-2 + atan(t))*((log(tan(t))*tan(t) + (1 + t^2)*atan(t)/cos(t)^2)^2 + (2 + 2*t^2)*tan(t)/cos(t)^2 - (1 + t^2)^2*atan(t)/cos(t)^4 - 2*t*tan(t)^2*log(tan(t)) + 2*(1 + t^2)^2*tan(t)^2*atan(t)/cos(t)^2)/(1 + t^2)^2
Denominador racional [src] 
              /        4                                    /        2 /        /                                                     2           2                                \           2              2                \               2                    \       \
   atan(t)    |/     2\     4    /         2   \   /     2\ |/     2\  |   2    |/                     /     2\ /       2   \        \    /     2\     2    /         2   \        |   /     2\  /       2   \     2           |       /     2\     4               |       |
tan       (t)*\\1 + t / *tan (t)*\2 + 2*tan (t)/ + \1 + t /*\\1 + t / *\tan (t)*\\log(tan(t))*tan(t) + \1 + t /*\1 + tan (t)/*atan(t)/  + \1 + t / *tan (t)*\2 + 2*tan (t)/*atan(t)/ - \1 + t / *\1 + tan (t)/ *tan (t)*atan(t)/ - 2*t*\1 + t / *tan (t)*log(tan(t))/*tan(t)/
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                      5                                                                                                                                      
                                                                                                                              /     2\     5                                                                                                                                 
                                                                                                                              \1 + t / *tan (t)
((t2+1)4(2tan⁡2(t)+2)tan⁡4(t)+(t2+1)(−2t(t2+1)2log⁡(tan⁡(t))tan⁡4(t)+(t2+1)2(−(t2+1)2(tan⁡2(t)+1)2tan⁡2(t)atan⁡(t)+((t2+1)2(2tan⁡2(t)+2)tan⁡2(t)atan⁡(t)+((t2+1)(tan⁡2(t)+1)atan⁡(t)+log⁡(tan⁡(t))tan⁡(t))2)tan⁡2(t)))tan⁡(t))tan⁡atan⁡(t)(t)(t2+1)5tan⁡5(t)\frac{\left(\left(t^{2} + 1\right)^{4} \left(2 \tan^{2}{\left(t \right)} + 2\right) \tan^{4}{\left(t \right)} + \left(t^{2} + 1\right) \left(- 2 t \left(t^{2} + 1\right)^{2} \log{\left(\tan{\left(t \right)} \right)} \tan^{4}{\left(t \right)} + \left(t^{2} + 1\right)^{2} \left(- \left(t^{2} + 1\right)^{2} \left(\tan^{2}{\left(t \right)} + 1\right)^{2} \tan^{2}{\left(t \right)} \operatorname{atan}{\left(t \right)} + \left(\left(t^{2} + 1\right)^{2} \left(2 \tan^{2}{\left(t \right)} + 2\right) \tan^{2}{\left(t \right)} \operatorname{atan}{\left(t \right)} + \left(\left(t^{2} + 1\right) \left(\tan^{2}{\left(t \right)} + 1\right) \operatorname{atan}{\left(t \right)} + \log{\left(\tan{\left(t \right)} \right)} \tan{\left(t \right)}\right)^{2}\right) \tan^{2}{\left(t \right)}\right)\right) \tan{\left(t \right)}\right) \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)}}{\left(t^{2} + 1\right)^{5} \tan^{5}{\left(t \right)}} 
tan(t)^atan(t)*((1 + t^2)^4*tan(t)^4*(2 + 2*tan(t)^2) + (1 + t^2)*((1 + t^2)^2*(tan(t)^2*((log(tan(t))*tan(t) + (1 + t^2)*(1 + tan(t)^2)*atan(t))^2 + (1 + t^2)^2*tan(t)^2*(2 + 2*tan(t)^2)*atan(t)) - (1 + t^2)^2*(1 + tan(t)^2)^2*tan(t)^2*atan(t)) - 2*t*(1 + t^2)^2*tan(t)^4*log(tan(t)))*tan(t))/((1 + t^2)^5*tan(t)^5)
Potencias [src] 
              /                                     2                                                            2                          \
              |/              /       2   \        \                                        2       /       2   \                           |
   atan(t)    ||log(tan(t))   \1 + tan (t)/*atan(t)|    /         2   \            2 + 2*tan (t)    \1 + tan (t)/ *atan(t)   2*t*log(tan(t))|
tan       (t)*||----------- + ---------------------|  + \2 + 2*tan (t)/*atan(t) + --------------- - ---------------------- - ---------------|
              ||        2             tan(t)       |                              /     2\                    2                         2   |
              |\   1 + t                           /                              \1 + t /*tan(t)          tan (t)              /     2\    |
              \                                                                                                                 \1 + t /    /
(−2tlog⁡(tan⁡(t))(t2+1)2+((tan⁡2(t)+1)atan⁡(t)tan⁡(t)+log⁡(tan⁡(t))t2+1)2−(tan⁡2(t)+1)2atan⁡(t)tan⁡2(t)+(2tan⁡2(t)+2)atan⁡(t)+2tan⁡2(t)+2(t2+1)tan⁡(t))tan⁡atan⁡(t)(t)\left(- \frac{2 t \log{\left(\tan{\left(t \right)} \right)}}{\left(t^{2} + 1\right)^{2}} + \left(\frac{\left(\tan^{2}{\left(t \right)} + 1\right) \operatorname{atan}{\left(t \right)}}{\tan{\left(t \right)}} + \frac{\log{\left(\tan{\left(t \right)} \right)}}{t^{2} + 1}\right)^{2} - \frac{\left(\tan^{2}{\left(t \right)} + 1\right)^{2} \operatorname{atan}{\left(t \right)}}{\tan^{2}{\left(t \right)}} + \left(2 \tan^{2}{\left(t \right)} + 2\right) \operatorname{atan}{\left(t \right)} + \frac{2 \tan^{2}{\left(t \right)} + 2}{\left(t^{2} + 1\right) \tan{\left(t \right)}}\right) \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} 
                            /                                                                            2                                                                                            2                                                                     \
                            |/                            /                    2\                       \                                                                      /                    2\                              /                      2\               |
                            ||                            |    /   I*t    -I*t\ |                       |                                                                      |    /   I*t    -I*t\ |                2             |      /   I*t    -I*t\ |               |
                            ||   /  /   I*t    -I*t\\     |    \- e    + e    / | / I*t    -I*t\        |                                               /  /   I*t    -I*t\\   |    \- e    + e    / |  / I*t    -I*t\              |    2*\- e    + e    / | / I*t    -I*t\|
                            ||   |I*\- e    + e    /|   I*|1 - -----------------|*\e    + e    /*atan(t)|                                               |I*\- e    + e    /|   |1 - -----------------| *\e    + e    / *atan(t)   I*|2 - -------------------|*\e    + e    /|
                    atan(t) ||log|------------------|     |                   2 |                       |    /                      2\           2*t*log|------------------|   |                   2 |                              |                    2  |               |
/  /   I*t    -I*t\\        ||   |    I*t    -I*t   |     |     / I*t    -I*t\  |                       |    |      /   I*t    -I*t\ |                  |    I*t    -I*t   |   |     / I*t    -I*t\  |                              |      / I*t    -I*t\   |               |
|I*\- e    + e    /|        ||   \   e    + e       /     \     \e    + e    /  /                       |    |    2*\- e    + e    / |                  \   e    + e       /   \     \e    + e    /  /                              \      \e    + e    /   /               |
|------------------|       *||----------------------- - ------------------------------------------------|  + |2 - -------------------|*atan(t) - --------------------------- + ------------------------------------------------ - ------------------------------------------|
|    I*t    -I*t   |        ||              2                               I*t    -I*t                 |    |                    2  |                            2                                           2                           /     2\ /   I*t    -I*t\         |
\   e    + e       /        |\         1 + t                             - e    + e                     /    |      / I*t    -I*t\   |                    /     2\                            /   I*t    -I*t\                            \1 + t /*\- e    + e    /         |
                            \                                                                                \      \e    + e    /   /                    \1 + t /                            \- e    + e    /                                                              /
(i(−eit+e−it)eit+e−it)atan⁡(t)(−2tlog⁡(i(−eit+e−it)eit+e−it)(t2+1)2+(−2(−eit+e−it)2(eit+e−it)2+2)atan⁡(t)+(−(−eit+e−it)2(eit+e−it)2+1)2(eit+e−it)2atan⁡(t)(−eit+e−it)2+(−i(−(−eit+e−it)2(eit+e−it)2+1)(eit+e−it)atan⁡(t)−eit+e−it+log⁡(i(−eit+e−it)eit+e−it)t2+1)2−i(−2(−eit+e−it)2(eit+e−it)2+2)(eit+e−it)(t2+1)(−eit+e−it))\left(\frac{i \left(- e^{i t} + e^{- i t}\right)}{e^{i t} + e^{- i t}}\right)^{\operatorname{atan}{\left(t \right)}} \left(- \frac{2 t \log{\left(\frac{i \left(- e^{i t} + e^{- i t}\right)}{e^{i t} + e^{- i t}} \right)}}{\left(t^{2} + 1\right)^{2}} + \left(- \frac{2 \left(- e^{i t} + e^{- i t}\right)^{2}}{\left(e^{i t} + e^{- i t}\right)^{2}} + 2\right) \operatorname{atan}{\left(t \right)} + \frac{\left(- \frac{\left(- e^{i t} + e^{- i t}\right)^{2}}{\left(e^{i t} + e^{- i t}\right)^{2}} + 1\right)^{2} \left(e^{i t} + e^{- i t}\right)^{2} \operatorname{atan}{\left(t \right)}}{\left(- e^{i t} + e^{- i t}\right)^{2}} + \left(- \frac{i \left(- \frac{\left(- e^{i t} + e^{- i t}\right)^{2}}{\left(e^{i t} + e^{- i t}\right)^{2}} + 1\right) \left(e^{i t} + e^{- i t}\right) \operatorname{atan}{\left(t \right)}}{- e^{i t} + e^{- i t}} + \frac{\log{\left(\frac{i \left(- e^{i t} + e^{- i t}\right)}{e^{i t} + e^{- i t}} \right)}}{t^{2} + 1}\right)^{2} - \frac{i \left(- \frac{2 \left(- e^{i t} + e^{- i t}\right)^{2}}{\left(e^{i t} + e^{- i t}\right)^{2}} + 2\right) \left(e^{i t} + e^{- i t}\right)}{\left(t^{2} + 1\right) \left(- e^{i t} + e^{- i t}\right)}\right) 
(i*(-exp(i*t) + exp(-i*t))/(exp(i*t) + exp(-i*t)))^atan(t)*((log(i*(-exp(i*t) + exp(-i*t))/(exp(i*t) + exp(-i*t)))/(1 + t^2) - i*(1 - (-exp(i*t) + exp(-i*t))^2/(exp(i*t) + exp(-i*t))^2)*(exp(i*t) + exp(-i*t))*atan(t)/(-exp(i*t) + exp(-i*t)))^2 + (2 - 2*(-exp(i*t) + exp(-i*t))^2/(exp(i*t) + exp(-i*t))^2)*atan(t) - 2*t*log(i*(-exp(i*t) + exp(-i*t))/(exp(i*t) + exp(-i*t)))/(1 + t^2)^2 + (1 - (-exp(i*t) + exp(-i*t))^2/(exp(i*t) + exp(-i*t))^2)^2*(exp(i*t) + exp(-i*t))^2*atan(t)/(-exp(i*t) + exp(-i*t))^2 - i*(2 - 2*(-exp(i*t) + exp(-i*t))^2/(exp(i*t) + exp(-i*t))^2)*(exp(i*t) + exp(-i*t))/((1 + t^2)*(-exp(i*t) + exp(-i*t))))
Unión de expresiones racionales [src] 
              /                                                     2           2              2                                                                                 2                              \
   atan(t)    |/                     /     2\ /       2   \        \    /     2\  /       2   \                   2                    /     2\ /       2   \            /     2\     2    /       2   \        |
tan       (t)*\\log(tan(t))*tan(t) + \1 + t /*\1 + tan (t)/*atan(t)/  - \1 + t / *\1 + tan (t)/ *atan(t) - 2*t*tan (t)*log(tan(t)) + 2*\1 + t /*\1 + tan (t)/*tan(t) + 2*\1 + t / *tan (t)*\1 + tan (t)/*atan(t)/
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                        2                                                                                                        
                                                                                                /     2\     2                                                                                                   
                                                                                                \1 + t / *tan (t)
(−2tlog⁡(tan⁡(t))tan⁡2(t)−(t2+1)2(tan⁡2(t)+1)2atan⁡(t)+2(t2+1)2(tan⁡2(t)+1)tan⁡2(t)atan⁡(t)+2(t2+1)(tan⁡2(t)+1)tan⁡(t)+((t2+1)(tan⁡2(t)+1)atan⁡(t)+log⁡(tan⁡(t))tan⁡(t))2)tan⁡atan⁡(t)(t)(t2+1)2tan⁡2(t)\frac{\left(- 2 t \log{\left(\tan{\left(t \right)} \right)} \tan^{2}{\left(t \right)} - \left(t^{2} + 1\right)^{2} \left(\tan^{2}{\left(t \right)} + 1\right)^{2} \operatorname{atan}{\left(t \right)} + 2 \left(t^{2} + 1\right)^{2} \left(\tan^{2}{\left(t \right)} + 1\right) \tan^{2}{\left(t \right)} \operatorname{atan}{\left(t \right)} + 2 \left(t^{2} + 1\right) \left(\tan^{2}{\left(t \right)} + 1\right) \tan{\left(t \right)} + \left(\left(t^{2} + 1\right) \left(\tan^{2}{\left(t \right)} + 1\right) \operatorname{atan}{\left(t \right)} + \log{\left(\tan{\left(t \right)} \right)} \tan{\left(t \right)}\right)^{2}\right) \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)}}{\left(t^{2} + 1\right)^{2} \tan^{2}{\left(t \right)}} 
tan(t)^atan(t)*((log(tan(t))*tan(t) + (1 + t^2)*(1 + tan(t)^2)*atan(t))^2 - (1 + t^2)^2*(1 + tan(t)^2)^2*atan(t) - 2*t*tan(t)^2*log(tan(t)) + 2*(1 + t^2)*(1 + tan(t)^2)*tan(t) + 2*(1 + t^2)^2*tan(t)^2*(1 + tan(t)^2)*atan(t))/((1 + t^2)^2*tan(t)^2)
Denominador común [src] 
    2       atan(t)         atan(t)                   3       atan(t)           atan(t)              4     2       atan(t)         2            2       atan(t)       4    atan(t)                 2    atan(t)                 2     2       atan(t)         2    3       atan(t)         2    atan(t)                    2       atan(t)                       3       atan(t)                               atan(t)                                    2    3       atan(t)                             2    atan(t)                                                                                                                          
atan (t)*tan       (t) - tan       (t)*atan(t) + 2*tan (t)*tan       (t) + 2*tan       (t)*tan(t) + t *atan (t)*tan       (t) + log (tan(t))*tan (t)*tan       (t) - t *tan       (t)*atan(t) - 2*t *tan       (t)*atan(t) + 2*t *atan (t)*tan       (t) + 2*t *tan (t)*tan       (t) + 2*t *tan       (t)*tan(t) - 2*t*tan (t)*tan       (t)*log(tan(t)) + 2*tan (t)*tan       (t)*atan(t)*log(tan(t)) + 2*tan       (t)*atan(t)*log(tan(t))*tan(t) + 2*t *tan (t)*tan       (t)*atan(t)*log(tan(t)) + 2*t *tan       (t)*atan(t)*log(tan(t))*tan(t)         2       atan(t)          2       2       atan(t)         2       atan(t)           
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + 2*atan (t)*tan       (t) + atan (t)*tan (t)*tan       (t) + tan (t)*tan       (t)*atan(t)
                                                                                                                                                                                                                                                            2       4    2         2    2                                                                                                                                                                                                                                                                                                                                                        
                                                                                                                                                                                                                                                         tan (t) + t *tan (t) + 2*t *tan (t)
tan⁡2(t)tan⁡atan⁡(t)(t)atan⁡2(t)+tan⁡2(t)tan⁡atan⁡(t)(t)atan⁡(t)+2tan⁡atan⁡(t)(t)atan⁡2(t)+t4tan⁡atan⁡(t)(t)atan⁡2(t)−t4tan⁡atan⁡(t)(t)atan⁡(t)+2t2log⁡(tan⁡(t))tan⁡3(t)tan⁡atan⁡(t)(t)atan⁡(t)+2t2log⁡(tan⁡(t))tan⁡(t)tan⁡atan⁡(t)(t)atan⁡(t)+2t2tan⁡3(t)tan⁡atan⁡(t)(t)+2t2tan⁡(t)tan⁡atan⁡(t)(t)+2t2tan⁡atan⁡(t)(t)atan⁡2(t)−2t2tan⁡atan⁡(t)(t)atan⁡(t)−2tlog⁡(tan⁡(t))tan⁡2(t)tan⁡atan⁡(t)(t)+log⁡(tan⁡(t))2tan⁡2(t)tan⁡atan⁡(t)(t)+2log⁡(tan⁡(t))tan⁡3(t)tan⁡atan⁡(t)(t)atan⁡(t)+2log⁡(tan⁡(t))tan⁡(t)tan⁡atan⁡(t)(t)atan⁡(t)+2tan⁡3(t)tan⁡atan⁡(t)(t)+2tan⁡(t)tan⁡atan⁡(t)(t)+tan⁡atan⁡(t)(t)atan⁡2(t)−tan⁡atan⁡(t)(t)atan⁡(t)t4tan⁡2(t)+2t2tan⁡2(t)+tan⁡2(t)\tan^{2}{\left(t \right)} \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} \operatorname{atan}^{2}{\left(t \right)} + \tan^{2}{\left(t \right)} \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} \operatorname{atan}{\left(t \right)} + 2 \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} \operatorname{atan}^{2}{\left(t \right)} + \frac{t^{4} \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} \operatorname{atan}^{2}{\left(t \right)} - t^{4} \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} \operatorname{atan}{\left(t \right)} + 2 t^{2} \log{\left(\tan{\left(t \right)} \right)} \tan^{3}{\left(t \right)} \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} \operatorname{atan}{\left(t \right)} + 2 t^{2} \log{\left(\tan{\left(t \right)} \right)} \tan{\left(t \right)} \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} \operatorname{atan}{\left(t \right)} + 2 t^{2} \tan^{3}{\left(t \right)} \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} + 2 t^{2} \tan{\left(t \right)} \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} + 2 t^{2} \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} \operatorname{atan}^{2}{\left(t \right)} - 2 t^{2} \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} \operatorname{atan}{\left(t \right)} - 2 t \log{\left(\tan{\left(t \right)} \right)} \tan^{2}{\left(t \right)} \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} + \log{\left(\tan{\left(t \right)} \right)}^{2} \tan^{2}{\left(t \right)} \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} + 2 \log{\left(\tan{\left(t \right)} \right)} \tan^{3}{\left(t \right)} \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} \operatorname{atan}{\left(t \right)} + 2 \log{\left(\tan{\left(t \right)} \right)} \tan{\left(t \right)} \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} \operatorname{atan}{\left(t \right)} + 2 \tan^{3}{\left(t \right)} \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} + 2 \tan{\left(t \right)} \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} + \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} \operatorname{atan}^{2}{\left(t \right)} - \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} \operatorname{atan}{\left(t \right)}}{t^{4} \tan^{2}{\left(t \right)} + 2 t^{2} \tan^{2}{\left(t \right)} + \tan^{2}{\left(t \right)}} 
(atan(t)^2*tan(t)^atan(t) - tan(t)^atan(t)*atan(t) + 2*tan(t)^3*tan(t)^atan(t) + 2*tan(t)^atan(t)*tan(t) + t^4*atan(t)^2*tan(t)^atan(t) + log(tan(t))^2*tan(t)^2*tan(t)^atan(t) - t^4*tan(t)^atan(t)*atan(t) - 2*t^2*tan(t)^atan(t)*atan(t) + 2*t^2*atan(t)^2*tan(t)^atan(t) + 2*t^2*tan(t)^3*tan(t)^atan(t) + 2*t^2*tan(t)^atan(t)*tan(t) - 2*t*tan(t)^2*tan(t)^atan(t)*log(tan(t)) + 2*tan(t)^3*tan(t)^atan(t)*atan(t)*log(tan(t)) + 2*tan(t)^atan(t)*atan(t)*log(tan(t))*tan(t) + 2*t^2*tan(t)^3*tan(t)^atan(t)*atan(t)*log(tan(t)) + 2*t^2*tan(t)^atan(t)*atan(t)*log(tan(t))*tan(t))/(tan(t)^2 + t^4*tan(t)^2 + 2*t^2*tan(t)^2) + 2*atan(t)^2*tan(t)^atan(t) + atan(t)^2*tan(t)^2*tan(t)^atan(t) + tan(t)^2*tan(t)^atan(t)*atan(t)
Compilar la expresión [src] 
              /                                     2                                                            2                          \
              |/              /       2   \        \                                        2       /       2   \                           |
   atan(t)    ||log(tan(t))   \1 + tan (t)/*atan(t)|    /         2   \            2 + 2*tan (t)    \1 + tan (t)/ *atan(t)   2*t*log(tan(t))|
tan       (t)*||----------- + ---------------------|  + \2 + 2*tan (t)/*atan(t) + --------------- - ---------------------- - ---------------|
              ||        2             tan(t)       |                              /     2\                    2                         2   |
              |\   1 + t                           /                              \1 + t /*tan(t)          tan (t)              /     2\    |
              \                                                                                                                 \1 + t /    /
(−2tlog⁡(tan⁡(t))(t2+1)2+((tan⁡2(t)+1)atan⁡(t)tan⁡(t)+log⁡(tan⁡(t))t2+1)2−(tan⁡2(t)+1)2atan⁡(t)tan⁡2(t)+(2tan⁡2(t)+2)atan⁡(t)+2tan⁡2(t)+2(t2+1)tan⁡(t))tan⁡atan⁡(t)(t)\left(- \frac{2 t \log{\left(\tan{\left(t \right)} \right)}}{\left(t^{2} + 1\right)^{2}} + \left(\frac{\left(\tan^{2}{\left(t \right)} + 1\right) \operatorname{atan}{\left(t \right)}}{\tan{\left(t \right)}} + \frac{\log{\left(\tan{\left(t \right)} \right)}}{t^{2} + 1}\right)^{2} - \frac{\left(\tan^{2}{\left(t \right)} + 1\right)^{2} \operatorname{atan}{\left(t \right)}}{\tan^{2}{\left(t \right)}} + \left(2 \tan^{2}{\left(t \right)} + 2\right) \operatorname{atan}{\left(t \right)} + \frac{2 \tan^{2}{\left(t \right)} + 2}{\left(t^{2} + 1\right) \tan{\left(t \right)}}\right) \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} 
tan(t)^atan(t)*((log(tan(t))/(1 + t^2) + (1 + tan(t)^2)*atan(t)/tan(t))^2 + (2 + 2*tan(t)^2)*atan(t) + (2 + 2*tan(t)^2)/((1 + t^2)*tan(t)) - (1 + tan(t)^2)^2*atan(t)/tan(t)^2 - 2*t*log(tan(t))/(1 + t^2)^2)
Abrimos la expresión [src] 
              /                                     2                                          2                                            \
              |/              /       2   \        \                              /       2   \                                /       2   \|
   atan(t)    ||log(tan(t))   \1 + tan (t)/*atan(t)|      /       2   \           \1 + tan (t)/ *atan(t)   2*t*log(tan(t))   2*\1 + tan (t)/|
tan       (t)*||----------- + ---------------------|  + 2*\1 + tan (t)/*atan(t) - ---------------------- - --------------- + ---------------|
              ||        2             tan(t)       |                                        2                         2      /     2\       |
              |\   1 + t                           /                                     tan (t)              /     2\       \1 + t /*tan(t)|
              \                                                                                               \1 + t /                      /
(−2tlog⁡(tan⁡(t))(t2+1)2−(tan⁡2(t)+1)2atan⁡(t)tan⁡2(t)+((tan⁡2(t)+1)atan⁡(t)tan⁡(t)+log⁡(tan⁡(t))t2+1)2+2(tan⁡2(t)+1)atan⁡(t)+2(tan⁡2(t)+1)(t2+1)tan⁡(t))tan⁡atan⁡(t)(t)\left(- \frac{2 t \log{\left(\tan{\left(t \right)} \right)}}{\left(t^{2} + 1\right)^{2}} - \frac{\left(\tan^{2}{\left(t \right)} + 1\right)^{2} \operatorname{atan}{\left(t \right)}}{\tan^{2}{\left(t \right)}} + \left(\frac{\left(\tan^{2}{\left(t \right)} + 1\right) \operatorname{atan}{\left(t \right)}}{\tan{\left(t \right)}} + \frac{\log{\left(\tan{\left(t \right)} \right)}}{t^{2} + 1}\right)^{2} + 2 \left(\tan^{2}{\left(t \right)} + 1\right) \operatorname{atan}{\left(t \right)} + \frac{2 \left(\tan^{2}{\left(t \right)} + 1\right)}{\left(t^{2} + 1\right) \tan{\left(t \right)}}\right) \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} 
      atan(t)                                      2            atan(t)          2       atan(t)                                                                          atan(t)                   2       atan(t)             atan(t)                       atan(t)                               2       atan(t)                       
 2*tan       (t)           2       atan(t)      log (tan(t))*tan       (t)   atan (t)*tan       (t)       2       2       atan(t)         2       atan(t)              tan       (t)*atan(t)   2*tan (t)*tan       (t)   2*t*tan       (t)*log(tan(t))   2*tan       (t)*atan(t)*log(tan(t))   2*tan (t)*tan       (t)*atan(t)*log(tan(t))
------------------ + 2*atan (t)*tan       (t) + -------------------------- + ---------------------- + atan (t)*tan (t)*tan       (t) + tan (t)*tan       (t)*atan(t) - --------------------- + ----------------------- - ----------------------------- + ----------------------------------- + -------------------------------------------
 2                                                         4      2                    2                                                                                         2                 2                                  4      2                     2                                         2                            
t *tan(t) + tan(t)                                    1 + t  + 2*t                  tan (t)                                                                                   tan (t)             t *tan(t) + tan(t)             1 + t  + 2*t                     t *tan(t) + tan(t)                        t *tan(t) + tan(t)
−2tlog⁡(tan⁡(t))tan⁡atan⁡(t)(t)t4+2t2+1+tan⁡2(t)tan⁡atan⁡(t)(t)atan⁡2(t)+tan⁡2(t)tan⁡atan⁡(t)(t)atan⁡(t)+2tan⁡atan⁡(t)(t)atan⁡2(t)+tan⁡atan⁡(t)(t)atan⁡2(t)tan⁡2(t)−tan⁡atan⁡(t)(t)atan⁡(t)tan⁡2(t)+log⁡(tan⁡(t))2tan⁡atan⁡(t)(t)t4+2t2+1+2log⁡(tan⁡(t))tan⁡2(t)tan⁡atan⁡(t)(t)atan⁡(t)t2tan⁡(t)+tan⁡(t)+2log⁡(tan⁡(t))tan⁡atan⁡(t)(t)atan⁡(t)t2tan⁡(t)+tan⁡(t)+2tan⁡2(t)tan⁡atan⁡(t)(t)t2tan⁡(t)+tan⁡(t)+2tan⁡atan⁡(t)(t)t2tan⁡(t)+tan⁡(t)- \frac{2 t \log{\left(\tan{\left(t \right)} \right)} \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)}}{t^{4} + 2 t^{2} + 1} + \tan^{2}{\left(t \right)} \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} \operatorname{atan}^{2}{\left(t \right)} + \tan^{2}{\left(t \right)} \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} \operatorname{atan}{\left(t \right)} + 2 \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} \operatorname{atan}^{2}{\left(t \right)} + \frac{\tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} \operatorname{atan}^{2}{\left(t \right)}}{\tan^{2}{\left(t \right)}} - \frac{\tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} \operatorname{atan}{\left(t \right)}}{\tan^{2}{\left(t \right)}} + \frac{\log{\left(\tan{\left(t \right)} \right)}^{2} \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)}}{t^{4} + 2 t^{2} + 1} + \frac{2 \log{\left(\tan{\left(t \right)} \right)} \tan^{2}{\left(t \right)} \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} \operatorname{atan}{\left(t \right)}}{t^{2} \tan{\left(t \right)} + \tan{\left(t \right)}} + \frac{2 \log{\left(\tan{\left(t \right)} \right)} \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} \operatorname{atan}{\left(t \right)}}{t^{2} \tan{\left(t \right)} + \tan{\left(t \right)}} + \frac{2 \tan^{2}{\left(t \right)} \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)}}{t^{2} \tan{\left(t \right)} + \tan{\left(t \right)}} + \frac{2 \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)}}{t^{2} \tan{\left(t \right)} + \tan{\left(t \right)}} 
2*tan(t)^atan(t)/(t^2*tan(t) + tan(t)) + 2*atan(t)^2*tan(t)^atan(t) + log(tan(t))^2*tan(t)^atan(t)/(1 + t^4 + 2*t^2) + atan(t)^2*tan(t)^atan(t)/tan(t)^2 + atan(t)^2*tan(t)^2*tan(t)^atan(t) + tan(t)^2*tan(t)^atan(t)*atan(t) - tan(t)^atan(t)*atan(t)/tan(t)^2 + 2*tan(t)^2*tan(t)^atan(t)/(t^2*tan(t) + tan(t)) - 2*t*tan(t)^atan(t)*log(tan(t))/(1 + t^4 + 2*t^2) + 2*tan(t)^atan(t)*atan(t)*log(tan(t))/(t^2*tan(t) + tan(t)) + 2*tan(t)^2*tan(t)^atan(t)*atan(t)*log(tan(t))/(t^2*tan(t) + tan(t))
Combinatoria [src] 
   atan(t)    /    2                     3                  4     2          2       4         2            2         4               4              2              2     2         2    3         2                2       2       4     2       4       4    4                     2                     2     2       4         2    4                 4     2       2           3                                                            2     2       2         2    3                             2                           \
tan       (t)*\atan (t) - atan(t) + 2*tan (t) + 2*tan(t) + t *atan (t) + atan (t)*tan (t) + log (tan(t))*tan (t) + tan (t)*atan(t) - t *atan(t) - 2*t *atan(t) + 2*t *atan (t) + 2*t *tan (t) + 2*t *tan(t) + 2*atan (t)*tan (t) + t *atan (t)*tan (t) + t *tan (t)*atan(t) - 2*t*tan (t)*log(tan(t)) + 2*t *atan (t)*tan (t) + 2*t *tan (t)*atan(t) + 2*t *atan (t)*tan (t) + 2*tan (t)*atan(t)*log(tan(t)) + 2*atan(t)*log(tan(t))*tan(t) + 4*t *atan (t)*tan (t) + 2*t *tan (t)*atan(t)*log(tan(t)) + 2*t *atan(t)*log(tan(t))*tan(t)/
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                                                                                                                                                                                                                                                            /     2\     2                                                                                                                                                                                                                                                               
                                                                                                                                                                                                                                                            \1 + t / *tan (t)
(t4tan⁡4(t)atan⁡2(t)+t4tan⁡4(t)atan⁡(t)+2t4tan⁡2(t)atan⁡2(t)+t4atan⁡2(t)−t4atan⁡(t)+2t2log⁡(tan⁡(t))tan⁡3(t)atan⁡(t)+2t2log⁡(tan⁡(t))tan⁡(t)atan⁡(t)+2t2tan⁡4(t)atan⁡2(t)+2t2tan⁡4(t)atan⁡(t)+2t2tan⁡3(t)+4t2tan⁡2(t)atan⁡2(t)+2t2tan⁡(t)+2t2atan⁡2(t)−2t2atan⁡(t)−2tlog⁡(tan⁡(t))tan⁡2(t)+log⁡(tan⁡(t))2tan⁡2(t)+2log⁡(tan⁡(t))tan⁡3(t)atan⁡(t)+2log⁡(tan⁡(t))tan⁡(t)atan⁡(t)+tan⁡4(t)atan⁡2(t)+tan⁡4(t)atan⁡(t)+2tan⁡3(t)+2tan⁡2(t)atan⁡2(t)+2tan⁡(t)+atan⁡2(t)−atan⁡(t))tan⁡atan⁡(t)(t)(t2+1)2tan⁡2(t)\frac{\left(t^{4} \tan^{4}{\left(t \right)} \operatorname{atan}^{2}{\left(t \right)} + t^{4} \tan^{4}{\left(t \right)} \operatorname{atan}{\left(t \right)} + 2 t^{4} \tan^{2}{\left(t \right)} \operatorname{atan}^{2}{\left(t \right)} + t^{4} \operatorname{atan}^{2}{\left(t \right)} - t^{4} \operatorname{atan}{\left(t \right)} + 2 t^{2} \log{\left(\tan{\left(t \right)} \right)} \tan^{3}{\left(t \right)} \operatorname{atan}{\left(t \right)} + 2 t^{2} \log{\left(\tan{\left(t \right)} \right)} \tan{\left(t \right)} \operatorname{atan}{\left(t \right)} + 2 t^{2} \tan^{4}{\left(t \right)} \operatorname{atan}^{2}{\left(t \right)} + 2 t^{2} \tan^{4}{\left(t \right)} \operatorname{atan}{\left(t \right)} + 2 t^{2} \tan^{3}{\left(t \right)} + 4 t^{2} \tan^{2}{\left(t \right)} \operatorname{atan}^{2}{\left(t \right)} + 2 t^{2} \tan{\left(t \right)} + 2 t^{2} \operatorname{atan}^{2}{\left(t \right)} - 2 t^{2} \operatorname{atan}{\left(t \right)} - 2 t \log{\left(\tan{\left(t \right)} \right)} \tan^{2}{\left(t \right)} + \log{\left(\tan{\left(t \right)} \right)}^{2} \tan^{2}{\left(t \right)} + 2 \log{\left(\tan{\left(t \right)} \right)} \tan^{3}{\left(t \right)} \operatorname{atan}{\left(t \right)} + 2 \log{\left(\tan{\left(t \right)} \right)} \tan{\left(t \right)} \operatorname{atan}{\left(t \right)} + \tan^{4}{\left(t \right)} \operatorname{atan}^{2}{\left(t \right)} + \tan^{4}{\left(t \right)} \operatorname{atan}{\left(t \right)} + 2 \tan^{3}{\left(t \right)} + 2 \tan^{2}{\left(t \right)} \operatorname{atan}^{2}{\left(t \right)} + 2 \tan{\left(t \right)} + \operatorname{atan}^{2}{\left(t \right)} - \operatorname{atan}{\left(t \right)}\right) \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)}}{\left(t^{2} + 1\right)^{2} \tan^{2}{\left(t \right)}} 
tan(t)^atan(t)*(atan(t)^2 - atan(t) + 2*tan(t)^3 + 2*tan(t) + t^4*atan(t)^2 + atan(t)^2*tan(t)^4 + log(tan(t))^2*tan(t)^2 + tan(t)^4*atan(t) - t^4*atan(t) - 2*t^2*atan(t) + 2*t^2*atan(t)^2 + 2*t^2*tan(t)^3 + 2*t^2*tan(t) + 2*atan(t)^2*tan(t)^2 + t^4*atan(t)^2*tan(t)^4 + t^4*tan(t)^4*atan(t) - 2*t*tan(t)^2*log(tan(t)) + 2*t^2*atan(t)^2*tan(t)^4 + 2*t^2*tan(t)^4*atan(t) + 2*t^4*atan(t)^2*tan(t)^2 + 2*tan(t)^3*atan(t)*log(tan(t)) + 2*atan(t)*log(tan(t))*tan(t) + 4*t^2*atan(t)^2*tan(t)^2 + 2*t^2*tan(t)^3*atan(t)*log(tan(t)) + 2*t^2*atan(t)*log(tan(t))*tan(t))/((1 + t^2)^2*tan(t)^2)
Respuesta numérica [src] 
tan(t)^atan(t)*((log(tan(t))/(1.0 + t^2) + (1.0 + tan(t)^2)*atan(t)/tan(t))^2 + (2.0 + 2.0*tan(t)^2)*atan(t) + (2.0 + 2.0*tan(t)^2)/((1.0 + t^2)*tan(t)) - (1.0 + tan(t)^2)^2*atan(t)/tan(t)^2 - 2.0*t*log(tan(t))/(1.0 + t^2)^2)
tan(t)^atan(t)*((log(tan(t))/(1.0 + t^2) + (1.0 + tan(t)^2)*atan(t)/tan(t))^2 + (2.0 + 2.0*tan(t)^2)*atan(t) + (2.0 + 2.0*tan(t)^2)/((1.0 + t^2)*tan(t)) - (1.0 + tan(t)^2)^2*atan(t)/tan(t)^2 - 2.0*t*log(tan(t))/(1.0 + t^2)^2)
    © Sr Examen – Калькулятор