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Simplificación de expresiones/ Descomposición en fracciones simples/ cos(x)*log(atan(sqrt(sin(x))))/((1+sin(x))*atan(sqrt(sin(x)))*sqrt(sin(x)))

¿Cómo vas a descomponer esta cos(x)*log(atan(sqrt(sin(x))))/((1+sin(x))*atan(sqrt(sin(x)))*sqrt(sin(x))) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
                /    /  ________\\      
      cos(x)*log\atan\\/ sin(x) //      
----------------------------------------
                 /  ________\   ________
(1 + sin(x))*atan\\/ sin(x) /*\/ sin(x)
log⁡(atan⁡(sin⁡(x)))cos⁡(x)(sin⁡(x)+1)atan⁡(sin⁡(x))sin⁡(x)\frac{\log{\left(\operatorname{atan}{\left(\sqrt{\sin{\left(x \right)}} \right)} \right)} \cos{\left(x \right)}}{\left(\sin{\left(x \right)} + 1\right) \operatorname{atan}{\left(\sqrt{\sin{\left(x \right)}} \right)} \sqrt{\sin{\left(x \right)}}} 
(cos(x)*log(atan(sqrt(sin(x)))))/((((1 + sin(x))*atan(sqrt(sin(x))))*sqrt(sin(x))))
Simplificación general [src] 
                /    /  ________\\      
      cos(x)*log\atan\\/ sin(x) //      
----------------------------------------
                 /  ________\   ________
(1 + sin(x))*atan\\/ sin(x) /*\/ sin(x)
log⁡(atan⁡(sin⁡(x)))cos⁡(x)(sin⁡(x)+1)sin⁡(x)atan⁡(sin⁡(x))\frac{\log{\left(\operatorname{atan}{\left(\sqrt{\sin{\left(x \right)}} \right)} \right)} \cos{\left(x \right)}}{\left(\sin{\left(x \right)} + 1\right) \sqrt{\sin{\left(x \right)}} \operatorname{atan}{\left(\sqrt{\sin{\left(x \right)}} \right)}} 
cos(x)*log(atan(sqrt(sin(x))))/((1 + sin(x))*atan(sqrt(sin(x)))*sqrt(sin(x)))
Respuesta numérica [src] 
sin(x)^(-0.5)*cos(x)*log(atan(sqrt(sin(x))))/((1.0 + sin(x))*atan(sqrt(sin(x))))
sin(x)^(-0.5)*cos(x)*log(atan(sqrt(sin(x))))/((1.0 + sin(x))*atan(sqrt(sin(x))))
Unión de expresiones racionales [src] 
                /    /  ________\\      
      cos(x)*log\atan\\/ sin(x) //      
----------------------------------------
                 /  ________\   ________
(1 + sin(x))*atan\\/ sin(x) /*\/ sin(x)
log⁡(atan⁡(sin⁡(x)))cos⁡(x)(sin⁡(x)+1)sin⁡(x)atan⁡(sin⁡(x))\frac{\log{\left(\operatorname{atan}{\left(\sqrt{\sin{\left(x \right)}} \right)} \right)} \cos{\left(x \right)}}{\left(\sin{\left(x \right)} + 1\right) \sqrt{\sin{\left(x \right)}} \operatorname{atan}{\left(\sqrt{\sin{\left(x \right)}} \right)}} 
cos(x)*log(atan(sqrt(sin(x))))/((1 + sin(x))*atan(sqrt(sin(x)))*sqrt(sin(x)))
Denominador común [src] 
                        /    /  ________\\              
              cos(x)*log\atan\\/ sin(x) //              
--------------------------------------------------------
  ________     /  ________\      3/2        /  ________\
\/ sin(x) *atan\\/ sin(x) / + sin   (x)*atan\\/ sin(x) /
log⁡(atan⁡(sin⁡(x)))cos⁡(x)sin⁡32(x)atan⁡(sin⁡(x))+sin⁡(x)atan⁡(sin⁡(x))\frac{\log{\left(\operatorname{atan}{\left(\sqrt{\sin{\left(x \right)}} \right)} \right)} \cos{\left(x \right)}}{\sin^{\frac{3}{2}}{\left(x \right)} \operatorname{atan}{\left(\sqrt{\sin{\left(x \right)}} \right)} + \sqrt{\sin{\left(x \right)}} \operatorname{atan}{\left(\sqrt{\sin{\left(x \right)}} \right)}} 
cos(x)*log(atan(sqrt(sin(x))))/(sqrt(sin(x))*atan(sqrt(sin(x))) + sin(x)^(3/2)*atan(sqrt(sin(x))))
Potencias [src] 
                                    /    /         _____________________\\            
                  / I*x    -I*x\    |    |  ___   /    /   -I*x    I*x\ ||            
              ___ |e      e    |    |    |\/ 2 *\/  -I*\- e     + e   / ||            
            \/ 2 *|---- + -----|*log|atan|------------------------------||            
                  \ 2       2  /    \    \              2               //            
--------------------------------------------------------------------------------------
                                                      /         _____________________\
   _____________________ /      /   -I*x    I*x\\     |  ___   /    /   -I*x    I*x\ |
  /    /   -I*x    I*x\  |    I*\- e     + e   /|     |\/ 2 *\/  -I*\- e     + e   / |
\/  -I*\- e     + e   / *|1 - ------------------|*atan|------------------------------|
                         \            2         /     \              2               /
2(eix2+e−ix2)log⁡(atan⁡(2−i(eix−e−ix)2))−i(eix−e−ix)(−i(eix−e−ix)2+1)atan⁡(2−i(eix−e−ix)2)\frac{\sqrt{2} \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right) \log{\left(\operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{- i \left(e^{i x} - e^{- i x}\right)}}{2} \right)} \right)}}{\sqrt{- i \left(e^{i x} - e^{- i x}\right)} \left(- \frac{i \left(e^{i x} - e^{- i x}\right)}{2} + 1\right) \operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{- i \left(e^{i x} - e^{- i x}\right)}}{2} \right)}} 
                /    /  ________\\      
      cos(x)*log\atan\\/ sin(x) //      
----------------------------------------
                 /  ________\   ________
(1 + sin(x))*atan\\/ sin(x) /*\/ sin(x)
log⁡(atan⁡(sin⁡(x)))cos⁡(x)(sin⁡(x)+1)sin⁡(x)atan⁡(sin⁡(x))\frac{\log{\left(\operatorname{atan}{\left(\sqrt{\sin{\left(x \right)}} \right)} \right)} \cos{\left(x \right)}}{\left(\sin{\left(x \right)} + 1\right) \sqrt{\sin{\left(x \right)}} \operatorname{atan}{\left(\sqrt{\sin{\left(x \right)}} \right)}} 
cos(x)*log(atan(sqrt(sin(x))))/((1 + sin(x))*atan(sqrt(sin(x)))*sqrt(sin(x)))
Denominador racional [src] 
  ________           /    /  ________\\
\/ sin(x) *cos(x)*log\atan\\/ sin(x) //
---------------------------------------
                   /  ________\        
  (1 + sin(x))*atan\\/ sin(x) /*sin(x)
log⁡(atan⁡(sin⁡(x)))sin⁡(x)cos⁡(x)(sin⁡(x)+1)sin⁡(x)atan⁡(sin⁡(x))\frac{\log{\left(\operatorname{atan}{\left(\sqrt{\sin{\left(x \right)}} \right)} \right)} \sqrt{\sin{\left(x \right)}} \cos{\left(x \right)}}{\left(\sin{\left(x \right)} + 1\right) \sin{\left(x \right)} \operatorname{atan}{\left(\sqrt{\sin{\left(x \right)}} \right)}} 
sqrt(sin(x))*cos(x)*log(atan(sqrt(sin(x))))/((1 + sin(x))*atan(sqrt(sin(x)))*sin(x))
Compilar la expresión [src] 
                /    /  ________\\      
      cos(x)*log\atan\\/ sin(x) //      
----------------------------------------
                 /  ________\   ________
(1 + sin(x))*atan\\/ sin(x) /*\/ sin(x)
log⁡(atan⁡(sin⁡(x)))cos⁡(x)(sin⁡(x)+1)sin⁡(x)atan⁡(sin⁡(x))\frac{\log{\left(\operatorname{atan}{\left(\sqrt{\sin{\left(x \right)}} \right)} \right)} \cos{\left(x \right)}}{\left(\sin{\left(x \right)} + 1\right) \sqrt{\sin{\left(x \right)}} \operatorname{atan}{\left(\sqrt{\sin{\left(x \right)}} \right)}} 
cos(x)*log(atan(sqrt(sin(x))))/((1 + sin(x))*atan(sqrt(sin(x)))*sqrt(sin(x)))
Parte trigonométrica [src] 
                                       /    /              _____________\\               
                                       |    |             /       /x\   ||               
                                       |    |            /     tan|-|   ||               
                  ___ /       2/x\\    |    |  ___      /         \2/   ||               
                \/ 2 *|1 - tan |-||*log|atan|\/ 2 *    /    ----------- ||               
                      \        \2//    |    |         /            2/x\ ||               
                                       |    |        /      1 + tan |-| ||               
                                       \    \      \/               \2/ //               
-----------------------------------------------------------------------------------------
          _____________                                     /              _____________\
         /       /x\                  /           /x\ \     |             /       /x\   |
        /     tan|-|                  |      2*tan|-| |     |            /     tan|-|   |
       /         \2/    /       2/x\\ |           \2/ |     |  ___      /         \2/   |
2*    /    ----------- *|1 + tan |-||*|1 + -----------|*atan|\/ 2 *    /    ----------- |
     /            2/x\  \        \2// |           2/x\|     |         /            2/x\ |
    /      1 + tan |-|                |    1 + tan |-||     |        /      1 + tan |-| |
  \/               \2/                \            \2//     \      \/               \2/ /
2(1−tan⁡2(x2))log⁡(atan⁡(2tan⁡(x2)tan⁡2(x2)+1))2tan⁡(x2)tan⁡2(x2)+1(1+2tan⁡(x2)tan⁡2(x2)+1)(tan⁡2(x2)+1)atan⁡(2tan⁡(x2)tan⁡2(x2)+1)\frac{\sqrt{2} \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) \log{\left(\operatorname{atan}{\left(\sqrt{2} \sqrt{\frac{\tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}} \right)} \right)}}{2 \sqrt{\frac{\tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}} \left(1 + \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right) \operatorname{atan}{\left(\sqrt{2} \sqrt{\frac{\tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}} \right)}} 
                 /    /    ________\\              
                 |    |   /   1    ||              
              log|atan|  /  ------ ||              
                 \    \\/   csc(x) //              
---------------------------------------------------
    ________                  /    ________\       
   /   1     /      1   \     |   /   1    |       
  /  ------ *|1 + ------|*atan|  /  ------ |*sec(x)
\/   csc(x)  \    csc(x)/     \\/   csc(x) /
log⁡(atan⁡(1csc⁡(x)))(1+1csc⁡(x))1csc⁡(x)atan⁡(1csc⁡(x))sec⁡(x)\frac{\log{\left(\operatorname{atan}{\left(\sqrt{\frac{1}{\csc{\left(x \right)}}} \right)} \right)}}{\left(1 + \frac{1}{\csc{\left(x \right)}}\right) \sqrt{\frac{1}{\csc{\left(x \right)}}} \operatorname{atan}{\left(\sqrt{\frac{1}{\csc{\left(x \right)}}} \right)} \sec{\left(x \right)}} 
                                /    /      _____________\\    
    /   1           1      \    |    |     /      1      ||    
    |------- - ------------|*log|atan|    /  ----------- ||    
    |   2/x\      2/x   pi\|    |    |   /      /    pi\ ||    
    |sec |-|   sec |- - --||    |    |  /    sec|x - --| ||    
    \    \2/       \2   2 //    \    \\/        \    2 / //    
---------------------------------------------------------------
      _____________                       /      _____________\
     /      1       /         1     \     |     /      1      |
    /  ----------- *|1 + -----------|*atan|    /  ----------- |
   /      /    pi\  |       /    pi\|     |   /      /    pi\ |
  /    sec|x - --|  |    sec|x - --||     |  /    sec|x - --| |
\/        \    2 /  \       \    2 //     \\/        \    2 / /
(−1sec⁡2(x2−π2)+1sec⁡2(x2))log⁡(atan⁡(1sec⁡(x−π2)))(1+1sec⁡(x−π2))1sec⁡(x−π2)atan⁡(1sec⁡(x−π2))\frac{\left(- \frac{1}{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + \frac{1}{\sec^{2}{\left(\frac{x}{2} \right)}}\right) \log{\left(\operatorname{atan}{\left(\sqrt{\frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}} \right)} \right)}}{\left(1 + \frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}\right) \sqrt{\frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}} \operatorname{atan}{\left(\sqrt{\frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}} \right)}} 
/   2/x\      2/x\\    /    /  ________\\
|cos |-| - sin |-||*log\atan\\/ sin(x) //
\    \2/       \2//                      
-----------------------------------------
                  /  ________\   ________
 (1 + sin(x))*atan\\/ sin(x) /*\/ sin(x)
(−sin⁡2(x2)+cos⁡2(x2))log⁡(atan⁡(sin⁡(x)))(sin⁡(x)+1)sin⁡(x)atan⁡(sin⁡(x))\frac{\left(- \sin^{2}{\left(\frac{x}{2} \right)} + \cos^{2}{\left(\frac{x}{2} \right)}\right) \log{\left(\operatorname{atan}{\left(\sqrt{\sin{\left(x \right)}} \right)} \right)}}{\left(\sin{\left(x \right)} + 1\right) \sqrt{\sin{\left(x \right)}} \operatorname{atan}{\left(\sqrt{\sin{\left(x \right)}} \right)}} 
                            /    /    ________\\
/     1            1   \    |    |   /   1    ||
|------------ - -------|*log|atan|  /  ------ ||
|   2/pi   x\      2/x\|    \    \\/   csc(x) //
|csc |-- - -|   csc |-||                        
\    \2    2/       \2//                        
------------------------------------------------
      ________                  /    ________\  
     /   1     /      1   \     |   /   1    |  
    /  ------ *|1 + ------|*atan|  /  ------ |  
  \/   csc(x)  \    csc(x)/     \\/   csc(x) /
(1csc⁡2(−x2+π2)−1csc⁡2(x2))log⁡(atan⁡(1csc⁡(x)))(1+1csc⁡(x))1csc⁡(x)atan⁡(1csc⁡(x))\frac{\left(\frac{1}{\csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}} - \frac{1}{\csc^{2}{\left(\frac{x}{2} \right)}}\right) \log{\left(\operatorname{atan}{\left(\sqrt{\frac{1}{\csc{\left(x \right)}}} \right)} \right)}}{\left(1 + \frac{1}{\csc{\left(x \right)}}\right) \sqrt{\frac{1}{\csc{\left(x \right)}}} \operatorname{atan}{\left(\sqrt{\frac{1}{\csc{\left(x \right)}}} \right)}} 
      /             2                 \    /    /              _____________\\
      |/       2/x\\           2/x\   |    |    |             /       /x\   ||
      ||1 - tan |-||      4*tan |-|   |    |    |            /     tan|-|   ||
  ___ |\        \4//            \4/   |    |    |  ___      /         \2/   ||
\/ 2 *|-------------- - --------------|*log|atan|\/ 2 *    /    ----------- ||
      |             2                2|    |    |         /            2/x\ ||
      |/       2/x\\    /       2/x\\ |    |    |        /      1 + tan |-| ||
      ||1 + tan |-||    |1 + tan |-|| |    \    \      \/               \2/ //
      \\        \4//    \        \4// /                                       
------------------------------------------------------------------------------
           _____________                       /              _____________\  
          /       /x\    /           /x\ \     |             /       /x\   |  
         /     tan|-|    |      2*tan|-| |     |            /     tan|-|   |  
        /         \2/    |           \2/ |     |  ___      /         \2/   |  
 2*    /    ----------- *|1 + -----------|*atan|\/ 2 *    /    ----------- |  
      /            2/x\  |           2/x\|     |         /            2/x\ |  
     /      1 + tan |-|  |    1 + tan |-||     |        /      1 + tan |-| |  
   \/               \2/  \            \2//     \      \/               \2/ /
2((1−tan⁡2(x4))2(tan⁡2(x4)+1)2−4tan⁡2(x4)(tan⁡2(x4)+1)2)log⁡(atan⁡(2tan⁡(x2)tan⁡2(x2)+1))2tan⁡(x2)tan⁡2(x2)+1(1+2tan⁡(x2)tan⁡2(x2)+1)atan⁡(2tan⁡(x2)tan⁡2(x2)+1)\frac{\sqrt{2} \left(\frac{\left(1 - \tan^{2}{\left(\frac{x}{4} \right)}\right)^{2}}{\left(\tan^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2}} - \frac{4 \tan^{2}{\left(\frac{x}{4} \right)}}{\left(\tan^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2}}\right) \log{\left(\operatorname{atan}{\left(\sqrt{2} \sqrt{\frac{\tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}} \right)} \right)}}{2 \sqrt{\frac{\tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}} \left(1 + \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right) \operatorname{atan}{\left(\sqrt{2} \sqrt{\frac{\tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}} \right)}} 
                                       /    /              _____________\\               
                                       |    |             /       /x\   ||               
                                       |    |            /     cot|-|   ||               
                 ___ /        2/x\\    |    |  ___      /         \2/   ||               
               \/ 2 *|-1 + cot |-||*log|atan|\/ 2 *    /    ----------- ||               
                     \         \2//    |    |         /            2/x\ ||               
                                       |    |        /      1 + cot |-| ||               
                                       \    \      \/               \2/ //               
-----------------------------------------------------------------------------------------
          _____________                                     /              _____________\
         /       /x\                  /           /x\ \     |             /       /x\   |
        /     cot|-|                  |      2*cot|-| |     |            /     cot|-|   |
       /         \2/    /       2/x\\ |           \2/ |     |  ___      /         \2/   |
2*    /    ----------- *|1 + cot |-||*|1 + -----------|*atan|\/ 2 *    /    ----------- |
     /            2/x\  \        \2// |           2/x\|     |         /            2/x\ |
    /      1 + cot |-|                |    1 + cot |-||     |        /      1 + cot |-| |
  \/               \2/                \            \2//     \      \/               \2/ /
2(cot⁡2(x2)−1)log⁡(atan⁡(2cot⁡(x2)cot⁡2(x2)+1))2cot⁡(x2)cot⁡2(x2)+1(1+2cot⁡(x2)cot⁡2(x2)+1)(cot⁡2(x2)+1)atan⁡(2cot⁡(x2)cot⁡2(x2)+1)\frac{\sqrt{2} \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right) \log{\left(\operatorname{atan}{\left(\sqrt{2} \sqrt{\frac{\cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}} \right)} \right)}}{2 \sqrt{\frac{\cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}} \left(1 + \frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \operatorname{atan}{\left(\sqrt{2} \sqrt{\frac{\cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}} \right)}} 
/   2/pi   x\      2/x\\    /    /  ________\\
|sin |-- + -| - sin |-||*log\atan\\/ sin(x) //
\    \2    2/       \2//                      
----------------------------------------------
                    /  ________\   ________   
   (1 + sin(x))*atan\\/ sin(x) /*\/ sin(x)
(−sin⁡2(x2)+sin⁡2(x2+π2))log⁡(atan⁡(sin⁡(x)))(sin⁡(x)+1)sin⁡(x)atan⁡(sin⁡(x))\frac{\left(- \sin^{2}{\left(\frac{x}{2} \right)} + \sin^{2}{\left(\frac{x}{2} + \frac{\pi}{2} \right)}\right) \log{\left(\operatorname{atan}{\left(\sqrt{\sin{\left(x \right)}} \right)} \right)}}{\left(\sin{\left(x \right)} + 1\right) \sqrt{\sin{\left(x \right)}} \operatorname{atan}{\left(\sqrt{\sin{\left(x \right)}} \right)}} 
      /              2                 \    /    /              _____________\\
      |/        2/x\\           2/x\   |    |    |             /       /x\   ||
      ||-1 + cot |-||      4*cot |-|   |    |    |            /     cot|-|   ||
  ___ |\         \4//            \4/   |    |    |  ___      /         \2/   ||
\/ 2 *|--------------- - --------------|*log|atan|\/ 2 *    /    ----------- ||
      |              2                2|    |    |         /            2/x\ ||
      | /       2/x\\    /       2/x\\ |    |    |        /      1 + cot |-| ||
      | |1 + cot |-||    |1 + cot |-|| |    \    \      \/               \2/ //
      \ \        \4//    \        \4// /                                       
-------------------------------------------------------------------------------
            _____________                       /              _____________\  
           /       /x\    /           /x\ \     |             /       /x\   |  
          /     cot|-|    |      2*cot|-| |     |            /     cot|-|   |  
         /         \2/    |           \2/ |     |  ___      /         \2/   |  
  2*    /    ----------- *|1 + -----------|*atan|\/ 2 *    /    ----------- |  
       /            2/x\  |           2/x\|     |         /            2/x\ |  
      /      1 + cot |-|  |    1 + cot |-||     |        /      1 + cot |-| |  
    \/               \2/  \            \2//     \      \/               \2/ /
2((cot⁡2(x4)−1)2(cot⁡2(x4)+1)2−4cot⁡2(x4)(cot⁡2(x4)+1)2)log⁡(atan⁡(2cot⁡(x2)cot⁡2(x2)+1))2cot⁡(x2)cot⁡2(x2)+1(1+2cot⁡(x2)cot⁡2(x2)+1)atan⁡(2cot⁡(x2)cot⁡2(x2)+1)\frac{\sqrt{2} \left(\frac{\left(\cot^{2}{\left(\frac{x}{4} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2}} - \frac{4 \cot^{2}{\left(\frac{x}{4} \right)}}{\left(\cot^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2}}\right) \log{\left(\operatorname{atan}{\left(\sqrt{2} \sqrt{\frac{\cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}} \right)} \right)}}{2 \sqrt{\frac{\cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}} \left(1 + \frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right) \operatorname{atan}{\left(\sqrt{2} \sqrt{\frac{\cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}} \right)}} 
                      /    /    _____________\\            
                      |    |   /    /    pi\ ||            
            cos(x)*log|atan|  /  cos|x - --| ||            
                      \    \\/      \    2 / //            
-----------------------------------------------------------
                      /    _____________\     _____________
/       /    pi\\     |   /    /    pi\ |    /    /    pi\ 
|1 + cos|x - --||*atan|  /  cos|x - --| |*  /  cos|x - --| 
\       \    2 //     \\/      \    2 / / \/      \    2 /
log⁡(atan⁡(cos⁡(x−π2)))cos⁡(x)(cos⁡(x−π2)+1)cos⁡(x−π2)atan⁡(cos⁡(x−π2))\frac{\log{\left(\operatorname{atan}{\left(\sqrt{\cos{\left(x - \frac{\pi}{2} \right)}} \right)} \right)} \cos{\left(x \right)}}{\left(\cos{\left(x - \frac{\pi}{2} \right)} + 1\right) \sqrt{\cos{\left(x - \frac{\pi}{2} \right)}} \operatorname{atan}{\left(\sqrt{\cos{\left(x - \frac{\pi}{2} \right)}} \right)}} 
                               /    /    _____________\\   
   /   2/x\      2/x   pi\\    |    |   /    /    pi\ ||   
   |cos |-| - cos |- - --||*log|atan|  /  cos|x - --| ||   
   \    \2/       \2   2 //    \    \\/      \    2 / //   
-----------------------------------------------------------
                      /    _____________\     _____________
/       /    pi\\     |   /    /    pi\ |    /    /    pi\ 
|1 + cos|x - --||*atan|  /  cos|x - --| |*  /  cos|x - --| 
\       \    2 //     \\/      \    2 / / \/      \    2 /
(cos⁡2(x2)−cos⁡2(x2−π2))log⁡(atan⁡(cos⁡(x−π2)))(cos⁡(x−π2)+1)cos⁡(x−π2)atan⁡(cos⁡(x−π2))\frac{\left(\cos^{2}{\left(\frac{x}{2} \right)} - \cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}\right) \log{\left(\operatorname{atan}{\left(\sqrt{\cos{\left(x - \frac{\pi}{2} \right)}} \right)} \right)}}{\left(\cos{\left(x - \frac{\pi}{2} \right)} + 1\right) \sqrt{\cos{\left(x - \frac{\pi}{2} \right)}} \operatorname{atan}{\left(\sqrt{\cos{\left(x - \frac{\pi}{2} \right)}} \right)}} 
                       /    /      _____________\\                    
                       |    |     /      1      ||                    
                    log|atan|    /  ----------- ||                    
                       |    |   /      /    pi\ ||                    
                       |    |  /    sec|x - --| ||                    
                       \    \\/        \    2 / //                    
----------------------------------------------------------------------
      _____________                       /      _____________\       
     /      1       /         1     \     |     /      1      |       
    /  ----------- *|1 + -----------|*atan|    /  ----------- |*sec(x)
   /      /    pi\  |       /    pi\|     |   /      /    pi\ |       
  /    sec|x - --|  |    sec|x - --||     |  /    sec|x - --| |       
\/        \    2 /  \       \    2 //     \\/        \    2 / /
log⁡(atan⁡(1sec⁡(x−π2)))(1+1sec⁡(x−π2))1sec⁡(x−π2)atan⁡(1sec⁡(x−π2))sec⁡(x)\frac{\log{\left(\operatorname{atan}{\left(\sqrt{\frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}} \right)} \right)}}{\left(1 + \frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}\right) \sqrt{\frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}} \operatorname{atan}{\left(\sqrt{\frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}} \right)} \sec{\left(x \right)}} 
                   /    /    ________\\                 
                   |    |   /   1    ||                 
                log|atan|  /  ------ ||                 
                   \    \\/   csc(x) //                 
--------------------------------------------------------
    ________                  /    ________\            
   /   1     /      1   \     |   /   1    |    /pi    \
  /  ------ *|1 + ------|*atan|  /  ------ |*csc|-- - x|
\/   csc(x)  \    csc(x)/     \\/   csc(x) /    \2     /
log⁡(atan⁡(1csc⁡(x)))(1+1csc⁡(x))1csc⁡(x)atan⁡(1csc⁡(x))csc⁡(−x+π2)\frac{\log{\left(\operatorname{atan}{\left(\sqrt{\frac{1}{\csc{\left(x \right)}}} \right)} \right)}}{\left(1 + \frac{1}{\csc{\left(x \right)}}\right) \sqrt{\frac{1}{\csc{\left(x \right)}}} \operatorname{atan}{\left(\sqrt{\frac{1}{\csc{\left(x \right)}}} \right)} \csc{\left(- x + \frac{\pi}{2} \right)}} 
      /    /  ________\\    /    pi\    
   log\atan\\/ sin(x) //*sin|x + --|    
                            \    2 /    
----------------------------------------
                 /  ________\   ________
(1 + sin(x))*atan\\/ sin(x) /*\/ sin(x)
log⁡(atan⁡(sin⁡(x)))sin⁡(x+π2)(sin⁡(x)+1)sin⁡(x)atan⁡(sin⁡(x))\frac{\log{\left(\operatorname{atan}{\left(\sqrt{\sin{\left(x \right)}} \right)} \right)} \sin{\left(x + \frac{\pi}{2} \right)}}{\left(\sin{\left(x \right)} + 1\right) \sqrt{\sin{\left(x \right)}} \operatorname{atan}{\left(\sqrt{\sin{\left(x \right)}} \right)}} 
                /    /  ________\\      
      cos(x)*log\atan\\/ sin(x) //      
----------------------------------------
                 /  ________\   ________
(1 + sin(x))*atan\\/ sin(x) /*\/ sin(x)
log⁡(atan⁡(sin⁡(x)))cos⁡(x)(sin⁡(x)+1)sin⁡(x)atan⁡(sin⁡(x))\frac{\log{\left(\operatorname{atan}{\left(\sqrt{\sin{\left(x \right)}} \right)} \right)} \cos{\left(x \right)}}{\left(\sin{\left(x \right)} + 1\right) \sqrt{\sin{\left(x \right)}} \operatorname{atan}{\left(\sqrt{\sin{\left(x \right)}} \right)}} 
cos(x)*log(atan(sqrt(sin(x))))/((1 + sin(x))*atan(sqrt(sin(x)))*sqrt(sin(x)))
Combinatoria [src] 
                /    /  ________\\      
      cos(x)*log\atan\\/ sin(x) //      
----------------------------------------
                 /  ________\   ________
(1 + sin(x))*atan\\/ sin(x) /*\/ sin(x)
log⁡(atan⁡(sin⁡(x)))cos⁡(x)(sin⁡(x)+1)sin⁡(x)atan⁡(sin⁡(x))\frac{\log{\left(\operatorname{atan}{\left(\sqrt{\sin{\left(x \right)}} \right)} \right)} \cos{\left(x \right)}}{\left(\sin{\left(x \right)} + 1\right) \sqrt{\sin{\left(x \right)}} \operatorname{atan}{\left(\sqrt{\sin{\left(x \right)}} \right)}} 
cos(x)*log(atan(sqrt(sin(x))))/((1 + sin(x))*atan(sqrt(sin(x)))*sqrt(sin(x)))
Abrimos la expresión [src] 
                        /    /  ________\\              
              cos(x)*log\atan\\/ sin(x) //              
--------------------------------------------------------
  ________     /  ________\      3/2        /  ________\
\/ sin(x) *atan\\/ sin(x) / + sin   (x)*atan\\/ sin(x) /
log⁡(atan⁡(sin⁡(x)))cos⁡(x)sin⁡32(x)atan⁡(sin⁡(x))+sin⁡(x)atan⁡(sin⁡(x))\frac{\log{\left(\operatorname{atan}{\left(\sqrt{\sin{\left(x \right)}} \right)} \right)} \cos{\left(x \right)}}{\sin^{\frac{3}{2}}{\left(x \right)} \operatorname{atan}{\left(\sqrt{\sin{\left(x \right)}} \right)} + \sqrt{\sin{\left(x \right)}} \operatorname{atan}{\left(\sqrt{\sin{\left(x \right)}} \right)}} 
                /    /  ________\\      
      cos(x)*log\atan\\/ sin(x) //      
----------------------------------------
                 /  ________\   ________
(1 + sin(x))*atan\\/ sin(x) /*\/ sin(x)
log⁡(atan⁡(sin⁡(x)))cos⁡(x)(sin⁡(x)+1)sin⁡(x)atan⁡(sin⁡(x))\frac{\log{\left(\operatorname{atan}{\left(\sqrt{\sin{\left(x \right)}} \right)} \right)} \cos{\left(x \right)}}{\left(\sin{\left(x \right)} + 1\right) \sqrt{\sin{\left(x \right)}} \operatorname{atan}{\left(\sqrt{\sin{\left(x \right)}} \right)}} 
cos(x)*log(atan(sqrt(sin(x))))/((1 + sin(x))*atan(sqrt(sin(x)))*sqrt(sin(x)))
    © Sr Examen – Калькулятор