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Simplificación de expresiones/ Descomposición en fracciones simples/ tan(7^x/2)/(2*log(7))-1/(2*log(7)*tan(7^x/2))

¿Cómo vas a descomponer esta tan(7^x/2)/(2*log(7))-1/(2*log(7)*tan(7^x/2)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   / x\                    
   |7 |                    
tan|--|                    
   \2 /           1        
-------- - ----------------
2*log(7)               / x\
                       |7 |
           2*log(7)*tan|--|
                       \2 /
tan⁡(7x2)2log⁡(7)−12log⁡(7)tan⁡(7x2)\frac{\tan{\left(\frac{7^{x}}{2} \right)}}{2 \log{\left(7 \right)}} - \frac{1}{2 \log{\left(7 \right)} \tan{\left(\frac{7^{x}}{2} \right)}} 
tan(7^x/2)/((2*log(7))) - 1/((2*log(7))*tan(7^x/2))
Simplificación general [src] 
               / x\
     1         |7 |
- ------- + tan|--|
     / x\      \2 /
     |7 |          
  tan|--|          
     \2 /          
-------------------
      2*log(7)
tan⁡(7x2)−1tan⁡(7x2)2log⁡(7)\frac{\tan{\left(\frac{7^{x}}{2} \right)} - \frac{1}{\tan{\left(\frac{7^{x}}{2} \right)}}}{2 \log{\left(7 \right)}} 
(-1/tan(7^x/2) + tan(7^x/2))/(2*log(7))
Respuesta numérica [src] 
0.256949171184875*tan(7^x/2) - 0.256949171184875/tan(7^x/2)
0.256949171184875*tan(7^x/2) - 0.256949171184875/tan(7^x/2)
Denominador racional [src] 
                  / x\       
                 2|7 |       
-2*log(7) + 2*tan |--|*log(7)
                  \2 /       
-----------------------------
                   / x\      
           2       |7 |      
      4*log (7)*tan|--|      
                   \2 /
2log⁡(7)tan⁡2(7x2)−2log⁡(7)4log⁡(7)2tan⁡(7x2)\frac{2 \log{\left(7 \right)} \tan^{2}{\left(\frac{7^{x}}{2} \right)} - 2 \log{\left(7 \right)}}{4 \log{\left(7 \right)}^{2} \tan{\left(\frac{7^{x}}{2} \right)}} 
(-2*log(7) + 2*tan(7^x/2)^2*log(7))/(4*log(7)^2*tan(7^x/2))
Denominador común [src] 
          / x\  
         2|7 |  
 -1 + tan |--|  
          \2 /  
----------------
            / x\
            |7 |
2*log(7)*tan|--|
            \2 /
tan⁡2(7x2)−12log⁡(7)tan⁡(7x2)\frac{\tan^{2}{\left(\frac{7^{x}}{2} \right)} - 1}{2 \log{\left(7 \right)} \tan{\left(\frac{7^{x}}{2} \right)}} 
(-1 + tan(7^x/2)^2)/(2*log(7)*tan(7^x/2))
Combinatoria [src] 
/       / x\\ /        / x\\
|       |7 || |        |7 ||
|1 + tan|--||*|-1 + tan|--||
\       \2 // \        \2 //
----------------------------
                  / x\      
                  |7 |      
      2*log(7)*tan|--|      
                  \2 /
(tan⁡(7x2)−1)(tan⁡(7x2)+1)2log⁡(7)tan⁡(7x2)\frac{\left(\tan{\left(\frac{7^{x}}{2} \right)} - 1\right) \left(\tan{\left(\frac{7^{x}}{2} \right)} + 1\right)}{2 \log{\left(7 \right)} \tan{\left(\frac{7^{x}}{2} \right)}} 
(1 + tan(7^x/2))*(-1 + tan(7^x/2))/(2*log(7)*tan(7^x/2))
Potencias [src] 
      /    x        x \            /      x        x \   
      | I*7     -I*7  |            |   I*7     -I*7  |   
      | ----    ------|            |   ----    ------|   
      |  2        2   |            |    2        2   |   
    I*\e     + e      /          I*\- e     + e      /   
---------------------------- + --------------------------
  /      x        x \            /    x        x \       
  |   I*7     -I*7  |            | I*7     -I*7  |       
  |   ----    ------|            | ----    ------|       
  |    2        2   |            |  2        2   |       
2*\- e     + e      /*log(7)   2*\e     + e      /*log(7)
i(−e7xi2+e−7xi2)2(e7xi2+e−7xi2)log⁡(7)+i(e7xi2+e−7xi2)2(−e7xi2+e−7xi2)log⁡(7)\frac{i \left(- e^{\frac{7^{x} i}{2}} + e^{- \frac{7^{x} i}{2}}\right)}{2 \left(e^{\frac{7^{x} i}{2}} + e^{- \frac{7^{x} i}{2}}\right) \log{\left(7 \right)}} + \frac{i \left(e^{\frac{7^{x} i}{2}} + e^{- \frac{7^{x} i}{2}}\right)}{2 \left(- e^{\frac{7^{x} i}{2}} + e^{- \frac{7^{x} i}{2}}\right) \log{\left(7 \right)}} 
i*(exp(i*7^x/2) + exp(-i*7^x/2))/(2*(-exp(i*7^x/2) + exp(-i*7^x/2))*log(7)) + i*(-exp(i*7^x/2) + exp(-i*7^x/2))/(2*(exp(i*7^x/2) + exp(-i*7^x/2))*log(7))
Parte trigonométrica [src] 
                       /        / x\\ 
                       |       2|7 || 
             2/ x\   2*|1 - tan |--|| 
      1 - tan \7 /     \        \2 // 
 -1 - ------------ + ---------------- 
             2/ x\             / x\   
      1 + tan \7 /            2|7 |   
                       1 + tan |--|   
                               \2 /   
--------------------------------------
/        / x\                 \       
|        |7 |                 |       
|   4*tan|--|           / x\  |       
|        \2 /      2*tan\7 /  |       
|- ------------ + ------------|*log(7)
|          / x\          2/ x\|       
|         2|7 |   1 + tan \7 /|       
|  1 + tan |--|               |       
\          \2 /               /
2(1−tan⁡2(7x2))tan⁡2(7x2)+1−1−tan⁡2(7x)tan⁡2(7x)+1−1(2tan⁡(7x)tan⁡2(7x)+1−4tan⁡(7x2)tan⁡2(7x2)+1)log⁡(7)\frac{\frac{2 \left(1 - \tan^{2}{\left(\frac{7^{x}}{2} \right)}\right)}{\tan^{2}{\left(\frac{7^{x}}{2} \right)} + 1} - \frac{1 - \tan^{2}{\left(7^{x} \right)}}{\tan^{2}{\left(7^{x} \right)} + 1} - 1}{\left(\frac{2 \tan{\left(7^{x} \right)}}{\tan^{2}{\left(7^{x} \right)} + 1} - \frac{4 \tan{\left(\frac{7^{x}}{2} \right)}}{\tan^{2}{\left(\frac{7^{x}}{2} \right)} + 1}\right) \log{\left(7 \right)}} 
             / x\
   1         |7 |
------- - cot|--|
   / x\      \2 /
   |7 |          
cot|--|          
   \2 /          
-----------------
     2*log(7)
−cot⁡(7x2)+1cot⁡(7x2)2log⁡(7)\frac{- \cot{\left(\frac{7^{x}}{2} \right)} + \frac{1}{\cot{\left(\frac{7^{x}}{2} \right)}}}{2 \log{\left(7 \right)}} 
       / x\               / x\     
       |7 |               |7 |     
    sin|--|            cos|--|     
       \2 /               \2 /     
---------------- - ----------------
     / x\                      / x\
     |7 |                      |7 |
2*cos|--|*log(7)   2*log(7)*sin|--|
     \2 /                      \2 /
sin⁡(7x2)2log⁡(7)cos⁡(7x2)−cos⁡(7x2)2log⁡(7)sin⁡(7x2)\frac{\sin{\left(\frac{7^{x}}{2} \right)}}{2 \log{\left(7 \right)} \cos{\left(\frac{7^{x}}{2} \right)}} - \frac{\cos{\left(\frac{7^{x}}{2} \right)}}{2 \log{\left(7 \right)} \sin{\left(\frac{7^{x}}{2} \right)}} 
     / x     \               / x\       
     |7    pi|               |7 |       
  cos|-- - --|            cos|--|       
     \2    2 /               \2 /       
---------------- - ---------------------
     / x\               / x     \       
     |7 |               |7    pi|       
2*cos|--|*log(7)   2*cos|-- - --|*log(7)
     \2 /               \2    2 /
−cos⁡(7x2)2log⁡(7)cos⁡(7x2−π2)+cos⁡(7x2−π2)2log⁡(7)cos⁡(7x2)- \frac{\cos{\left(\frac{7^{x}}{2} \right)}}{2 \log{\left(7 \right)} \cos{\left(\frac{7^{x}}{2} - \frac{\pi}{2} \right)}} + \frac{\cos{\left(\frac{7^{x}}{2} - \frac{\pi}{2} \right)}}{2 \log{\left(7 \right)} \cos{\left(\frac{7^{x}}{2} \right)}} 
                      / x\ 
                      |7 | 
                   cot|--| 
       1              \2 / 
---------------- - --------
     / x\          2*log(7)
     |7 |                  
2*cot|--|*log(7)           
     \2 /
−cot⁡(7x2)2log⁡(7)+12log⁡(7)cot⁡(7x2)- \frac{\cot{\left(\frac{7^{x}}{2} \right)}}{2 \log{\left(7 \right)}} + \frac{1}{2 \log{\left(7 \right)} \cot{\left(\frac{7^{x}}{2} \right)}} 
      / x\             
     2|7 |             
2*sin |--|       / x\  
      \2 /    sin\7 /  
---------- - ----------
    / x\           / x\
 sin\7 /          2|7 |
             2*sin |--|
                   \2 /
-----------------------
        2*log(7)
2sin⁡2(7x2)sin⁡(7x)−sin⁡(7x)2sin⁡2(7x2)2log⁡(7)\frac{\frac{2 \sin^{2}{\left(\frac{7^{x}}{2} \right)}}{\sin{\left(7^{x} \right)}} - \frac{\sin{\left(7^{x} \right)}}{2 \sin^{2}{\left(\frac{7^{x}}{2} \right)}}}{2 \log{\left(7 \right)}} 
       / x\               / x\     
       |7 |               |7 |     
    sec|--|            csc|--|     
       \2 /               \2 /     
---------------- - ----------------
     / x\                      / x\
     |7 |                      |7 |
2*csc|--|*log(7)   2*log(7)*sec|--|
     \2 /                      \2 /
−csc⁡(7x2)2log⁡(7)sec⁡(7x2)+sec⁡(7x2)2log⁡(7)csc⁡(7x2)- \frac{\csc{\left(\frac{7^{x}}{2} \right)}}{2 \log{\left(7 \right)} \sec{\left(\frac{7^{x}}{2} \right)}} + \frac{\sec{\left(\frac{7^{x}}{2} \right)}}{2 \log{\left(7 \right)} \csc{\left(\frac{7^{x}}{2} \right)}} 
    /       / x\\    / x\    
    \1 - cos\7 //*cos\7 /    
-----------------------------
/        / x\\           / x\
\-1 + cos\7 //*log(7)*sin\7 /
(1−cos⁡(7x))cos⁡(7x)(cos⁡(7x)−1)log⁡(7)sin⁡(7x)\frac{\left(1 - \cos{\left(7^{x} \right)}\right) \cos{\left(7^{x} \right)}}{\left(\cos{\left(7^{x} \right)} - 1\right) \log{\left(7 \right)} \sin{\left(7^{x} \right)}} 
           /   x\        / x\   
   -1 - cos\2*7 / + 2*cos\7 /   
--------------------------------
/       / x\      /   x\\       
\- 2*sin\7 / + sin\2*7 //*log(7)
2cos⁡(7x)−cos⁡(2⋅7x)−1(−2sin⁡(7x)+sin⁡(2⋅7x))log⁡(7)\frac{2 \cos{\left(7^{x} \right)} - \cos{\left(2 \cdot 7^{x} \right)} - 1}{\left(- 2 \sin{\left(7^{x} \right)} + \sin{\left(2 \cdot 7^{x} \right)}\right) \log{\left(7 \right)}} 
               / x\
     1         |7 |
- ------- + tan|--|
     / x\      \2 /
     |7 |          
  tan|--|          
     \2 /          
-------------------
      2*log(7)
tan⁡(7x2)−1tan⁡(7x2)2log⁡(7)\frac{\tan{\left(\frac{7^{x}}{2} \right)} - \frac{1}{\tan{\left(\frac{7^{x}}{2} \right)}}}{2 \log{\left(7 \right)}} 
                1          2          
       -1 - --------- + -------       
               /   x\      / x\       
            sec\2*7 /   sec\7 /       
--------------------------------------
/      1               2      \       
|-------------- - ------------|*log(7)
|   /   x   pi\      / x   pi\|       
|sec|2*7  - --|   sec|7  - --||       
\   \       2 /      \     2 //
−1−1sec⁡(2⋅7x)+2sec⁡(7x)(1sec⁡(2⋅7x−π2)−2sec⁡(7x−π2))log⁡(7)\frac{-1 - \frac{1}{\sec{\left(2 \cdot 7^{x} \right)}} + \frac{2}{\sec{\left(7^{x} \right)}}}{\left(\frac{1}{\sec{\left(2 \cdot 7^{x} - \frac{\pi}{2} \right)}} - \frac{2}{\sec{\left(7^{x} - \frac{\pi}{2} \right)}}\right) \log{\left(7 \right)}} 
   /      x\        / x\   
   |pi   7 |        |7 |   
csc|-- - --|     csc|--|   
   \2    2 /        \2 /   
------------ - ------------
     / x\         /      x\
     |7 |         |pi   7 |
  csc|--|      csc|-- - --|
     \2 /         \2    2 /
---------------------------
          2*log(7)
−csc⁡(7x2)csc⁡(−7x2+π2)+csc⁡(−7x2+π2)csc⁡(7x2)2log⁡(7)\frac{- \frac{\csc{\left(\frac{7^{x}}{2} \right)}}{\csc{\left(- \frac{7^{x}}{2} + \frac{\pi}{2} \right)}} + \frac{\csc{\left(- \frac{7^{x}}{2} + \frac{\pi}{2} \right)}}{\csc{\left(\frac{7^{x}}{2} \right)}}}{2 \log{\left(7 \right)}} 
        /pi      x\        / x   pi\
-1 - sin|-- + 2*7 | + 2*sin|7  + --|
        \2        /        \     2 /
------------------------------------
  /       / x\      /   x\\         
  \- 2*sin\7 / + sin\2*7 //*log(7)
2sin⁡(7x+π2)−sin⁡(2⋅7x+π2)−1(−2sin⁡(7x)+sin⁡(2⋅7x))log⁡(7)\frac{2 \sin{\left(7^{x} + \frac{\pi}{2} \right)} - \sin{\left(2 \cdot 7^{x} + \frac{\pi}{2} \right)} - 1}{\left(- 2 \sin{\left(7^{x} \right)} + \sin{\left(2 \cdot 7^{x} \right)}\right) \log{\left(7 \right)}} 
                      / x\
                     2|7 |
       / x\     2*sin |--|
    sin\7 /           \2 /
- ----------- + ----------
         / x\       / x\  
  1 - cos\7 /    sin\7 /  
--------------------------
         2*log(7)
2sin⁡2(7x2)sin⁡(7x)−sin⁡(7x)1−cos⁡(7x)2log⁡(7)\frac{\frac{2 \sin^{2}{\left(\frac{7^{x}}{2} \right)}}{\sin{\left(7^{x} \right)}} - \frac{\sin{\left(7^{x} \right)}}{1 - \cos{\left(7^{x} \right)}}}{2 \log{\left(7 \right)}} 
                       /         / x\\
                       |        2|7 ||
             2/ x\   2*|-1 + cot |--||
     -1 + cot \7 /     \         \2 //
-1 - ------------- + -----------------
             2/ x\              / x\  
      1 + cot \7 /             2|7 |  
                        1 + cot |--|  
                                \2 /  
--------------------------------------
/        / x\                 \       
|        |7 |                 |       
|   4*cot|--|           / x\  |       
|        \2 /      2*cot\7 /  |       
|- ------------ + ------------|*log(7)
|          / x\          2/ x\|       
|         2|7 |   1 + cot \7 /|       
|  1 + cot |--|               |       
\          \2 /               /
2(cot⁡2(7x2)−1)cot⁡2(7x2)+1−cot⁡2(7x)−1cot⁡2(7x)+1−1(2cot⁡(7x)cot⁡2(7x)+1−4cot⁡(7x2)cot⁡2(7x2)+1)log⁡(7)\frac{\frac{2 \left(\cot^{2}{\left(\frac{7^{x}}{2} \right)} - 1\right)}{\cot^{2}{\left(\frac{7^{x}}{2} \right)} + 1} - \frac{\cot^{2}{\left(7^{x} \right)} - 1}{\cot^{2}{\left(7^{x} \right)} + 1} - 1}{\left(\frac{2 \cot{\left(7^{x} \right)}}{\cot^{2}{\left(7^{x} \right)} + 1} - \frac{4 \cot{\left(\frac{7^{x}}{2} \right)}}{\cot^{2}{\left(\frac{7^{x}}{2} \right)} + 1}\right) \log{\left(7 \right)}} 
           1               2      
-1 - -------------- + ------------
        /pi      x\      /pi    x\
     csc|-- - 2*7 |   csc|-- - 7 |
        \2        /      \2      /
----------------------------------
   /    1          2   \          
   |--------- - -------|*log(7)   
   |   /   x\      / x\|          
   \csc\2*7 /   csc\7 //
−1+2csc⁡(−7x+π2)−1csc⁡(−2⋅7x+π2)(1csc⁡(2⋅7x)−2csc⁡(7x))log⁡(7)\frac{-1 + \frac{2}{\csc{\left(- 7^{x} + \frac{\pi}{2} \right)}} - \frac{1}{\csc{\left(- 2 \cdot 7^{x} + \frac{\pi}{2} \right)}}}{\left(\frac{1}{\csc{\left(2 \cdot 7^{x} \right)}} - \frac{2}{\csc{\left(7^{x} \right)}}\right) \log{\left(7 \right)}} 
          / x\               / x     \  
          |7 |               |7    pi|  
       sec|--|            sec|-- - --|  
          \2 /               \2    2 /  
--------------------- - ----------------
            / x     \               / x\
            |7    pi|               |7 |
2*log(7)*sec|-- - --|   2*log(7)*sec|--|
            \2    2 /               \2 /
sec⁡(7x2)2log⁡(7)sec⁡(7x2−π2)−sec⁡(7x2−π2)2log⁡(7)sec⁡(7x2)\frac{\sec{\left(\frac{7^{x}}{2} \right)}}{2 \log{\left(7 \right)} \sec{\left(\frac{7^{x}}{2} - \frac{\pi}{2} \right)}} - \frac{\sec{\left(\frac{7^{x}}{2} - \frac{\pi}{2} \right)}}{2 \log{\left(7 \right)} \sec{\left(\frac{7^{x}}{2} \right)}} 
       / x\                       
      2|7 |                       
   sin |--|              / x\     
       \2 /           sin\7 /     
-------------- - -----------------
          / x\                / x\
log(7)*sin\7 /               2|7 |
                 4*log(7)*sin |--|
                              \2 /
sin⁡2(7x2)log⁡(7)sin⁡(7x)−sin⁡(7x)4log⁡(7)sin⁡2(7x2)\frac{\sin^{2}{\left(\frac{7^{x}}{2} \right)}}{\log{\left(7 \right)} \sin{\left(7^{x} \right)}} - \frac{\sin{\left(7^{x} \right)}}{4 \log{\left(7 \right)} \sin^{2}{\left(\frac{7^{x}}{2} \right)}} 
     / x\         / x     \
     |7 |         |7    pi|
  sec|--|      sec|-- - --|
     \2 /         \2    2 /
------------ - ------------
   / x     \        / x\   
   |7    pi|        |7 |   
sec|-- - --|     sec|--|   
   \2    2 /        \2 /   
---------------------------
          2*log(7)
sec⁡(7x2)sec⁡(7x2−π2)−sec⁡(7x2−π2)sec⁡(7x2)2log⁡(7)\frac{\frac{\sec{\left(\frac{7^{x}}{2} \right)}}{\sec{\left(\frac{7^{x}}{2} - \frac{\pi}{2} \right)}} - \frac{\sec{\left(\frac{7^{x}}{2} - \frac{\pi}{2} \right)}}{\sec{\left(\frac{7^{x}}{2} \right)}}}{2 \log{\left(7 \right)}} 
   / x     \        / x\   
   |7    pi|        |7 |   
cos|-- - --|     cos|--|   
   \2    2 /        \2 /   
------------ - ------------
     / x\         / x     \
     |7 |         |7    pi|
  cos|--|      cos|-- - --|
     \2 /         \2    2 /
---------------------------
          2*log(7)
−cos⁡(7x2)cos⁡(7x2−π2)+cos⁡(7x2−π2)cos⁡(7x2)2log⁡(7)\frac{- \frac{\cos{\left(\frac{7^{x}}{2} \right)}}{\cos{\left(\frac{7^{x}}{2} - \frac{\pi}{2} \right)}} + \frac{\cos{\left(\frac{7^{x}}{2} - \frac{\pi}{2} \right)}}{\cos{\left(\frac{7^{x}}{2} \right)}}}{2 \log{\left(7 \right)}} 
     / x\      / x\
     |7 |      |7 |
- cot|--| + tan|--|
     \2 /      \2 /
-------------------
      2*log(7)
tan⁡(7x2)−cot⁡(7x2)2log⁡(7)\frac{\tan{\left(\frac{7^{x}}{2} \right)} - \cot{\left(\frac{7^{x}}{2} \right)}}{2 \log{\left(7 \right)}} 
                /   x\        / x\        
        -1 - cos\2*7 / + 2*cos\7 /        
------------------------------------------
/       / x   pi\      /   x   pi\\       
|- 2*cos|7  - --| + cos|2*7  - --||*log(7)
\       \     2 /      \       2 //
2cos⁡(7x)−cos⁡(2⋅7x)−1(−2cos⁡(7x−π2)+cos⁡(2⋅7x−π2))log⁡(7)\frac{2 \cos{\left(7^{x} \right)} - \cos{\left(2 \cdot 7^{x} \right)} - 1}{\left(- 2 \cos{\left(7^{x} - \frac{\pi}{2} \right)} + \cos{\left(2 \cdot 7^{x} - \frac{\pi}{2} \right)}\right) \log{\left(7 \right)}} 
     /      x\               / x\       
     |pi   7 |               |7 |       
  csc|-- - --|            csc|--|       
     \2    2 /               \2 /       
---------------- - ---------------------
     / x\               /      x\       
     |7 |               |pi   7 |       
2*csc|--|*log(7)   2*csc|-- - --|*log(7)
     \2 /               \2    2 /
−csc⁡(7x2)2log⁡(7)csc⁡(−7x2+π2)+csc⁡(−7x2+π2)2log⁡(7)csc⁡(7x2)- \frac{\csc{\left(\frac{7^{x}}{2} \right)}}{2 \log{\left(7 \right)} \csc{\left(- \frac{7^{x}}{2} + \frac{\pi}{2} \right)}} + \frac{\csc{\left(- \frac{7^{x}}{2} + \frac{\pi}{2} \right)}}{2 \log{\left(7 \right)} \csc{\left(\frac{7^{x}}{2} \right)}} 
csc(pi/2 - 7^x/2)/(2*csc(7^x/2)*log(7)) - csc(7^x/2)/(2*csc(pi/2 - 7^x/2)*log(7))
Unión de expresiones racionales [src] 
          / x\  
         2|7 |  
 -1 + tan |--|  
          \2 /  
----------------
            / x\
            |7 |
2*log(7)*tan|--|
            \2 /
tan⁡2(7x2)−12log⁡(7)tan⁡(7x2)\frac{\tan^{2}{\left(\frac{7^{x}}{2} \right)} - 1}{2 \log{\left(7 \right)} \tan{\left(\frac{7^{x}}{2} \right)}} 
(-1 + tan(7^x/2)^2)/(2*log(7)*tan(7^x/2))
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