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Simplificación de expresiones/ Descomposición en fracciones simples/ cos(x)^(x^2/(x+1))*((-x^2/(x+1)^2+2*x/(x+1))*log(cos(x))-x^2*sin(x)/((x+1)*cos(x)))

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

Expresión a simplificar:

Solución

Ha introducido [src] 
           2                                                   
          x                                                    
        ----- //    2           \                  2          \
        x + 1 ||  -x        2*x |                 x *sin(x)   |
(cos(x))     *||-------- + -----|*log(cos(x)) - --------------|
              ||       2   x + 1|               (x + 1)*cos(x)|
              \\(x + 1)         /                             /
(−x2sin⁡(x)(x+1)cos⁡(x)+(2xx+1+(−1)x2(x+1)2)log⁡(cos⁡(x)))cos⁡x2x+1(x)\left(- \frac{x^{2} \sin{\left(x \right)}}{\left(x + 1\right) \cos{\left(x \right)}} + \left(\frac{2 x}{x + 1} + \frac{\left(-1\right) x^{2}}{\left(x + 1\right)^{2}}\right) \log{\left(\cos{\left(x \right)} \right)}\right) \cos^{\frac{x^{2}}{x + 1}}{\left(x \right)} 
cos(x)^(x^2/(x + 1))*(((-x^2)/(x + 1)^2 + (2*x)/(x + 1))*log(cos(x)) - x^2*sin(x)/((x + 1)*cos(x)))
Simplificación general [src] 
                2                                                    
          -1 + x  - x                                                
          -----------                                                
             1 + x                                                   
x*(cos(x))           *((2 + x)*cos(x)*log(cos(x)) - x*(1 + x)*sin(x))
---------------------------------------------------------------------
                                      2                              
                               (1 + x)
x(−x(x+1)sin⁡(x)+(x+2)log⁡(cos⁡(x))cos⁡(x))cos⁡x2−x−1x+1(x)(x+1)2\frac{x \left(- x \left(x + 1\right) \sin{\left(x \right)} + \left(x + 2\right) \log{\left(\cos{\left(x \right)} \right)} \cos{\left(x \right)}\right) \cos^{\frac{x^{2} - x - 1}{x + 1}}{\left(x \right)}}{\left(x + 1\right)^{2}} 
x*cos(x)^((-1 + x^2 - x)/(1 + x))*((2 + x)*cos(x)*log(cos(x)) - x*(1 + x)*sin(x))/(1 + x)^2
Combinatoria [src] 
              2                                                                       
             x                                                                        
           -----                                                                      
           1 + x /            2                                                     \ 
-x*(cos(x))     *\x*sin(x) + x *sin(x) - 2*cos(x)*log(cos(x)) - x*cos(x)*log(cos(x))/ 
--------------------------------------------------------------------------------------
                                          2                                           
                                   (1 + x) *cos(x)
−x(x2sin⁡(x)−xlog⁡(cos⁡(x))cos⁡(x)+xsin⁡(x)−2log⁡(cos⁡(x))cos⁡(x))cos⁡x2x+1(x)(x+1)2cos⁡(x)- \frac{x \left(x^{2} \sin{\left(x \right)} - x \log{\left(\cos{\left(x \right)} \right)} \cos{\left(x \right)} + x \sin{\left(x \right)} - 2 \log{\left(\cos{\left(x \right)} \right)} \cos{\left(x \right)}\right) \cos^{\frac{x^{2}}{x + 1}}{\left(x \right)}}{\left(x + 1\right)^{2} \cos{\left(x \right)}} 
-x*cos(x)^(x^2/(1 + x))*(x*sin(x) + x^2*sin(x) - 2*cos(x)*log(cos(x)) - x*cos(x)*log(cos(x)))/((1 + x)^2*cos(x))
Respuesta numérica [src] 
cos(x)^(x^2/(1.0 + x))*((-x^2/(1.0 + x)^2 + 2.0*x/(1.0 + x))*log(cos(x)) - x^2*sin(x)/((1.0 + x)*cos(x)))
cos(x)^(x^2/(1.0 + x))*((-x^2/(1.0 + x)^2 + 2.0*x/(1.0 + x))*log(cos(x)) - x^2*sin(x)/((1.0 + x)*cos(x)))
Denominador racional [src] 
           2                                                                                   
          x                                                                                    
        -----                                                                                  
        x + 1 /   2        3                  /   2                      2\                   \
(cos(x))     *\- x *(1 + x) *sin(x) + (1 + x)*\- x *(1 + x) + 2*x*(1 + x) /*cos(x)*log(cos(x))/
-----------------------------------------------------------------------------------------------
                                               4                                               
                                        (1 + x) *cos(x)
(−x2(x+1)3sin⁡(x)+(x+1)(−x2(x+1)+2x(x+1)2)log⁡(cos⁡(x))cos⁡(x))cos⁡x2x+1(x)(x+1)4cos⁡(x)\frac{\left(- x^{2} \left(x + 1\right)^{3} \sin{\left(x \right)} + \left(x + 1\right) \left(- x^{2} \left(x + 1\right) + 2 x \left(x + 1\right)^{2}\right) \log{\left(\cos{\left(x \right)} \right)} \cos{\left(x \right)}\right) \cos^{\frac{x^{2}}{x + 1}}{\left(x \right)}}{\left(x + 1\right)^{4} \cos{\left(x \right)}} 
cos(x)^(x^2/(x + 1))*(-x^2*(1 + x)^3*sin(x) + (1 + x)*(-x^2*(1 + x) + 2*x*(1 + x)^2)*cos(x)*log(cos(x)))/((1 + x)^4*cos(x))
Denominador común [src] 
                                          2                         2                      2                    
           2                             x                         x                      x                     
          x                            -----                     -----                  -----                   
        -----                2         1 + x           3         1 + x                  1 + x                   
        1 + x               x *(cos(x))     *sin(x) + x *(cos(x))     *sin(x) + (cos(x))     *cos(x)*log(cos(x))
(cos(x))     *log(cos(x)) - ------------------------------------------------------------------------------------
                                                       2                                                        
                                                      x *cos(x) + 2*x*cos(x) + cos(x)
log⁡(cos⁡(x))cos⁡x2x+1(x)−x3sin⁡(x)cos⁡x2x+1(x)+x2sin⁡(x)cos⁡x2x+1(x)+log⁡(cos⁡(x))cos⁡(x)cos⁡x2x+1(x)x2cos⁡(x)+2xcos⁡(x)+cos⁡(x)\log{\left(\cos{\left(x \right)} \right)} \cos^{\frac{x^{2}}{x + 1}}{\left(x \right)} - \frac{x^{3} \sin{\left(x \right)} \cos^{\frac{x^{2}}{x + 1}}{\left(x \right)} + x^{2} \sin{\left(x \right)} \cos^{\frac{x^{2}}{x + 1}}{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)} \cos{\left(x \right)} \cos^{\frac{x^{2}}{x + 1}}{\left(x \right)}}{x^{2} \cos{\left(x \right)} + 2 x \cos{\left(x \right)} + \cos{\left(x \right)}} 
cos(x)^(x^2/(1 + x))*log(cos(x)) - (x^2*cos(x)^(x^2/(1 + x))*sin(x) + x^3*cos(x)^(x^2/(1 + x))*sin(x) + cos(x)^(x^2/(1 + x))*cos(x)*log(cos(x)))/(x^2*cos(x) + 2*x*cos(x) + cos(x))
Abrimos la expresión [src] 
                2                         2                               2             
               x                         x                               x              
             -----                     -----                           -----            
   2         x + 1           2         x + 1                           x + 1            
  x *(cos(x))     *sin(x)   x *(cos(x))     *log(cos(x))   2*x*(cos(x))     *log(cos(x))
- ----------------------- - ---------------------------- + -----------------------------
     x*cos(x) + cos(x)                   2                             x + 1            
                                    1 + x  + 2*x
−x2log⁡(cos⁡(x))cos⁡x2x+1(x)x2+2x+1−x2sin⁡(x)cos⁡x2x+1(x)xcos⁡(x)+cos⁡(x)+2xlog⁡(cos⁡(x))cos⁡x2x+1(x)x+1- \frac{x^{2} \log{\left(\cos{\left(x \right)} \right)} \cos^{\frac{x^{2}}{x + 1}}{\left(x \right)}}{x^{2} + 2 x + 1} - \frac{x^{2} \sin{\left(x \right)} \cos^{\frac{x^{2}}{x + 1}}{\left(x \right)}}{x \cos{\left(x \right)} + \cos{\left(x \right)}} + \frac{2 x \log{\left(\cos{\left(x \right)} \right)} \cos^{\frac{x^{2}}{x + 1}}{\left(x \right)}}{x + 1} 
-x^2*cos(x)^(x^2/(x + 1))*sin(x)/(x*cos(x) + cos(x)) - x^2*cos(x)^(x^2/(x + 1))*log(cos(x))/(1 + x^2 + 2*x) + 2*x*cos(x)^(x^2/(x + 1))*log(cos(x))/(x + 1)
Potencias [src] 
                 2                                                                     
                x                                                                      
              -----                                                                    
              1 + x                                                                    
/ I*x    -I*x\      //      2           \    / I*x    -I*x\       2 /   -I*x    I*x\  \
|e      e    |      ||     x        2*x |    |e      e    |    I*x *\- e     + e   /  |
|---- + -----|     *||- -------- + -----|*log|---- + -----| + ------------------------|
\ 2       2  /      ||         2   1 + x|    \ 2       2  /             / I*x    -I*x\|
                    |\  (1 + x)         /                               |e      e    ||
                    |                                         2*(1 + x)*|---- + -----||
                    \                                                   \ 2       2  //
(ix2(eix−e−ix)2(x+1)(eix2+e−ix2)+(−x2(x+1)2+2xx+1)log⁡(eix2+e−ix2))(eix2+e−ix2)x2x+1\left(\frac{i x^{2} \left(e^{i x} - e^{- i x}\right)}{2 \left(x + 1\right) \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)} + \left(- \frac{x^{2}}{\left(x + 1\right)^{2}} + \frac{2 x}{x + 1}\right) \log{\left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2} \right)}\right) \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)^{\frac{x^{2}}{x + 1}} 
           2                                                     
          x                                                      
        ----- //      2           \                  2          \
        1 + x ||     x        2*x |                 x *sin(x)   |
(cos(x))     *||- -------- + -----|*log(cos(x)) - --------------|
              ||         2   1 + x|               (1 + x)*cos(x)|
              \\  (1 + x)         /                             /
(−x2sin⁡(x)(x+1)cos⁡(x)+(−x2(x+1)2+2xx+1)log⁡(cos⁡(x)))cos⁡x2x+1(x)\left(- \frac{x^{2} \sin{\left(x \right)}}{\left(x + 1\right) \cos{\left(x \right)}} + \left(- \frac{x^{2}}{\left(x + 1\right)^{2}} + \frac{2 x}{x + 1}\right) \log{\left(\cos{\left(x \right)} \right)}\right) \cos^{\frac{x^{2}}{x + 1}}{\left(x \right)} 
cos(x)^(x^2/(1 + x))*((-x^2/(1 + x)^2 + 2*x/(1 + x))*log(cos(x)) - x^2*sin(x)/((1 + x)*cos(x)))
Parte trigonométrica [src] 
                2                                                               
               x                                                                
             -----                                                              
             1 + x //      2           \                          2            \
/   /    pi\\      ||     x        2*x |    /   /    pi\\        x *sin(x)     |
|sin|x + --||     *||- -------- + -----|*log|sin|x + --|| - -------------------|
\   \    2 //      ||         2   1 + x|    \   \    2 //              /    pi\|
                   |\  (1 + x)         /                    (1 + x)*sin|x + --||
                   \                                                   \    2 //
(−x2sin⁡(x)(x+1)sin⁡(x+π2)+(−x2(x+1)2+2xx+1)log⁡(sin⁡(x+π2)))sin⁡x2x+1(x+π2)\left(- \frac{x^{2} \sin{\left(x \right)}}{\left(x + 1\right) \sin{\left(x + \frac{\pi}{2} \right)}} + \left(- \frac{x^{2}}{\left(x + 1\right)^{2}} + \frac{2 x}{x + 1}\right) \log{\left(\sin{\left(x + \frac{\pi}{2} \right)} \right)}\right) \sin^{\frac{x^{2}}{x + 1}}{\left(x + \frac{\pi}{2} \right)} 
           2                                                     
          x   /                                    2    /    pi\\
        ----- |/      2           \               x *cos|x - --||
        1 + x ||     x        2*x |                     \    2 /|
(cos(x))     *||- -------- + -----|*log(cos(x)) - --------------|
              ||         2   1 + x|               (1 + x)*cos(x)|
              \\  (1 + x)         /                             /
(−x2cos⁡(x−π2)(x+1)cos⁡(x)+(−x2(x+1)2+2xx+1)log⁡(cos⁡(x)))cos⁡x2x+1(x)\left(- \frac{x^{2} \cos{\left(x - \frac{\pi}{2} \right)}}{\left(x + 1\right) \cos{\left(x \right)}} + \left(- \frac{x^{2}}{\left(x + 1\right)^{2}} + \frac{2 x}{x + 1}\right) \log{\left(\cos{\left(x \right)} \right)}\right) \cos^{\frac{x^{2}}{x + 1}}{\left(x \right)} 
                 2                                                                   
                x                                                                    
              -----                                                                  
              1 + x                                                                  
/        2/x\\      /                        /        2/x\\           2    /x\      \
|-1 + cot |-||      |/      2           \    |-1 + cot |-||        2*x *cot|-|      |
|         \2/|      ||     x        2*x |    |         \2/|                \2/      |
|------------|     *||- -------- + -----|*log|------------| - ----------------------|
|       2/x\ |      ||         2   1 + x|    |       2/x\ |           /        2/x\\|
|1 + cot |-| |      |\  (1 + x)         /    |1 + cot |-| |   (1 + x)*|-1 + cot |-|||
\        \2/ /      \                        \        \2/ /           \         \2///
(cot⁡2(x2)−1cot⁡2(x2)+1)x2x+1(−2x2cot⁡(x2)(x+1)(cot⁡2(x2)−1)+(−x2(x+1)2+2xx+1)log⁡(cot⁡2(x2)−1cot⁡2(x2)+1))\left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right)^{\frac{x^{2}}{x + 1}} \left(- \frac{2 x^{2} \cot{\left(\frac{x}{2} \right)}}{\left(x + 1\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)} + \left(- \frac{x^{2}}{\left(x + 1\right)^{2}} + \frac{2 x}{x + 1}\right) \log{\left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} \right)}\right) 
           2                                              
          x                                               
        ----- //    2           \                2       \
        x + 1 ||  -x        2*x |               x *tan(x)|
(cos(x))     *||-------- + -----|*log(cos(x)) - ---------|
              ||       2   x + 1|                 1 + x  |
              \\(x + 1)         /                        /
(−x2tan⁡(x)x+1+(2xx+1+(−1)x2(x+1)2)log⁡(cos⁡(x)))cos⁡x2x+1(x)\left(- \frac{x^{2} \tan{\left(x \right)}}{x + 1} + \left(\frac{2 x}{x + 1} + \frac{\left(-1\right) x^{2}}{\left(x + 1\right)^{2}}\right) \log{\left(\cos{\left(x \right)} \right)}\right) \cos^{\frac{x^{2}}{x + 1}}{\left(x \right)} 
                2                                                     
               x                                                      
             -----                                                    
             1 + x                                                    
/       2/x\\      /                        /       2/x\\            \
|1 - tan |-||      |/      2           \    |1 - tan |-||    2       |
|        \2/|      ||     x        2*x |    |        \2/|   x *tan(x)|
|-----------|     *||- -------- + -----|*log|-----------| - ---------|
|       2/x\|      ||         2   1 + x|    |       2/x\|     1 + x  |
|1 + tan |-||      |\  (1 + x)         /    |1 + tan |-||            |
\        \2//      \                        \        \2//            /
(1−tan⁡2(x2)tan⁡2(x2)+1)x2x+1(−x2tan⁡(x)x+1+(−x2(x+1)2+2xx+1)log⁡(1−tan⁡2(x2)tan⁡2(x2)+1))\left(\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right)^{\frac{x^{2}}{x + 1}} \left(- \frac{x^{2} \tan{\left(x \right)}}{x + 1} + \left(- \frac{x^{2}}{\left(x + 1\right)^{2}} + \frac{2 x}{x + 1}\right) \log{\left(\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} \right)}\right) 
           2                                                
          x                                                 
        ----- //      2           \                2       \
        1 + x ||     x        2*x |               x *tan(x)|
(cos(x))     *||- -------- + -----|*log(cos(x)) - ---------|
              ||         2   1 + x|                 1 + x  |
              \\  (1 + x)         /                        /
(−x2tan⁡(x)x+1+(−x2(x+1)2+2xx+1)log⁡(cos⁡(x)))cos⁡x2x+1(x)\left(- \frac{x^{2} \tan{\left(x \right)}}{x + 1} + \left(- \frac{x^{2}}{\left(x + 1\right)^{2}} + \frac{2 x}{x + 1}\right) \log{\left(\cos{\left(x \right)} \right)}\right) \cos^{\frac{x^{2}}{x + 1}}{\left(x \right)} 
                2                                                                 
               x                                                                  
             -----                                                                
             1 + x                                                                
/       2/x\\      /                        /       2/x\\           2    /x\     \
|1 - tan |-||      |/      2           \    |1 - tan |-||        2*x *tan|-|     |
|        \2/|      ||     x        2*x |    |        \2/|                \2/     |
|-----------|     *||- -------- + -----|*log|-----------| - ---------------------|
|       2/x\|      ||         2   1 + x|    |       2/x\|           /       2/x\\|
|1 + tan |-||      |\  (1 + x)         /    |1 + tan |-||   (1 + x)*|1 - tan |-|||
\        \2//      \                        \        \2//           \        \2///
(1−tan⁡2(x2)tan⁡2(x2)+1)x2x+1(−2x2tan⁡(x2)(1−tan⁡2(x2))(x+1)+(−x2(x+1)2+2xx+1)log⁡(1−tan⁡2(x2)tan⁡2(x2)+1))\left(\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right)^{\frac{x^{2}}{x + 1}} \left(- \frac{2 x^{2} \tan{\left(\frac{x}{2} \right)}}{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) \left(x + 1\right)} + \left(- \frac{x^{2}}{\left(x + 1\right)^{2}} + \frac{2 x}{x + 1}\right) \log{\left(\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} \right)}\right) 
                 2                                                           
                x                                                            
              -----                                                          
              1 + x                                                          
/        2/x\\      /                        /        2/x\\                 \
|-1 + cot |-||      |/      2           \    |-1 + cot |-||          2      |
|         \2/|      ||     x        2*x |    |         \2/|         x       |
|------------|     *||- -------- + -----|*log|------------| - --------------|
|       2/x\ |      ||         2   1 + x|    |       2/x\ |   (1 + x)*cot(x)|
|1 + cot |-| |      |\  (1 + x)         /    |1 + cot |-| |                 |
\        \2/ /      \                        \        \2/ /                 /
(cot⁡2(x2)−1cot⁡2(x2)+1)x2x+1(−x2(x+1)cot⁡(x)+(−x2(x+1)2+2xx+1)log⁡(cot⁡2(x2)−1cot⁡2(x2)+1))\left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right)^{\frac{x^{2}}{x + 1}} \left(- \frac{x^{2}}{\left(x + 1\right) \cot{\left(x \right)}} + \left(- \frac{x^{2}}{\left(x + 1\right)^{2}} + \frac{2 x}{x + 1}\right) \log{\left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} \right)}\right) 
           2                                                          
          x                                                           
        -----                                                         
        1 + x //      2           \                     2            \
/  1   \      ||     x        2*x |    /  1   \        x *sec(x)     |
|------|     *||- -------- + -----|*log|------| - -------------------|
\sec(x)/      ||         2   1 + x|    \sec(x)/              /    pi\|
              |\  (1 + x)         /               (1 + x)*sec|x - --||
              \                                              \    2 //
(−x2sec⁡(x)(x+1)sec⁡(x−π2)+(−x2(x+1)2+2xx+1)log⁡(1sec⁡(x)))(1sec⁡(x))x2x+1\left(- \frac{x^{2} \sec{\left(x \right)}}{\left(x + 1\right) \sec{\left(x - \frac{\pi}{2} \right)}} + \left(- \frac{x^{2}}{\left(x + 1\right)^{2}} + \frac{2 x}{x + 1}\right) \log{\left(\frac{1}{\sec{\left(x \right)}} \right)}\right) \left(\frac{1}{\sec{\left(x \right)}}\right)^{\frac{x^{2}}{x + 1}} 
           2                                                     
          x                                                      
        ----- //      2           \                  2          \
        1 + x ||     x        2*x |                 x *sin(x)   |
(cos(x))     *||- -------- + -----|*log(cos(x)) - --------------|
              ||         2   1 + x|               (1 + x)*cos(x)|
              \\  (1 + x)         /                             /
(−x2sin⁡(x)(x+1)cos⁡(x)+(−x2(x+1)2+2xx+1)log⁡(cos⁡(x)))cos⁡x2x+1(x)\left(- \frac{x^{2} \sin{\left(x \right)}}{\left(x + 1\right) \cos{\left(x \right)}} + \left(- \frac{x^{2}}{\left(x + 1\right)^{2}} + \frac{2 x}{x + 1}\right) \log{\left(\cos{\left(x \right)} \right)}\right) \cos^{\frac{x^{2}}{x + 1}}{\left(x \right)} 
                2                                                            
               x                                                             
             -----                                                           
             1 + x //      2           \                         2    2     \
/   /    pi\\      ||     x        2*x |    /   /    pi\\     2*x *sin (x)  |
|sin|x + --||     *||- -------- + -----|*log|sin|x + --|| - ----------------|
\   \    2 //      ||         2   1 + x|    \   \    2 //   (1 + x)*sin(2*x)|
                   \\  (1 + x)         /                                    /
(−2x2sin⁡2(x)(x+1)sin⁡(2x)+(−x2(x+1)2+2xx+1)log⁡(sin⁡(x+π2)))sin⁡x2x+1(x+π2)\left(- \frac{2 x^{2} \sin^{2}{\left(x \right)}}{\left(x + 1\right) \sin{\left(2 x \right)}} + \left(- \frac{x^{2}}{\left(x + 1\right)^{2}} + \frac{2 x}{x + 1}\right) \log{\left(\sin{\left(x + \frac{\pi}{2} \right)} \right)}\right) \sin^{\frac{x^{2}}{x + 1}}{\left(x + \frac{\pi}{2} \right)} 
                2                                                          
               x                                                           
             ----- /                                         2    /pi    \\
             1 + x |/      2           \                    x *csc|-- - x||
/     1     \      ||     x        2*x |    /     1     \         \2     /|
|-----------|     *||- -------- + -----|*log|-----------| - --------------|
|   /pi    \|      ||         2   1 + x|    |   /pi    \|   (1 + x)*csc(x)|
|csc|-- - x||      |\  (1 + x)         /    |csc|-- - x||                 |
\   \2     //      \                        \   \2     //                 /
(−x2csc⁡(−x+π2)(x+1)csc⁡(x)+(−x2(x+1)2+2xx+1)log⁡(1csc⁡(−x+π2)))(1csc⁡(−x+π2))x2x+1\left(- \frac{x^{2} \csc{\left(- x + \frac{\pi}{2} \right)}}{\left(x + 1\right) \csc{\left(x \right)}} + \left(- \frac{x^{2}}{\left(x + 1\right)^{2}} + \frac{2 x}{x + 1}\right) \log{\left(\frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}} \right)}\right) \left(\frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right)^{\frac{x^{2}}{x + 1}} 
           2                                                     
          x                                                      
        -----                                                    
        1 + x //      2           \                  2          \
/  1   \      ||     x        2*x |    /  1   \     x *sec(x)   |
|------|     *||- -------- + -----|*log|------| - --------------|
\sec(x)/      ||         2   1 + x|    \sec(x)/   (1 + x)*csc(x)|
              \\  (1 + x)         /                             /
(−x2sec⁡(x)(x+1)csc⁡(x)+(−x2(x+1)2+2xx+1)log⁡(1sec⁡(x)))(1sec⁡(x))x2x+1\left(- \frac{x^{2} \sec{\left(x \right)}}{\left(x + 1\right) \csc{\left(x \right)}} + \left(- \frac{x^{2}}{\left(x + 1\right)^{2}} + \frac{2 x}{x + 1}\right) \log{\left(\frac{1}{\sec{\left(x \right)}} \right)}\right) \left(\frac{1}{\sec{\left(x \right)}}\right)^{\frac{x^{2}}{x + 1}} 
(1/sec(x))^(x^2/(1 + x))*((-x^2/(1 + x)^2 + 2*x/(1 + x))*log(1/sec(x)) - x^2*sec(x)/((1 + x)*csc(x)))
Unión de expresiones racionales [src] 
             2                                                 
            x                                                  
          -----                                                
          1 + x                                                
x*(cos(x))     *((2 + x)*cos(x)*log(cos(x)) - x*(1 + x)*sin(x))
---------------------------------------------------------------
                               2                               
                        (1 + x) *cos(x)
x(−x(x+1)sin⁡(x)+(x+2)log⁡(cos⁡(x))cos⁡(x))cos⁡x2x+1(x)(x+1)2cos⁡(x)\frac{x \left(- x \left(x + 1\right) \sin{\left(x \right)} + \left(x + 2\right) \log{\left(\cos{\left(x \right)} \right)} \cos{\left(x \right)}\right) \cos^{\frac{x^{2}}{x + 1}}{\left(x \right)}}{\left(x + 1\right)^{2} \cos{\left(x \right)}} 
x*cos(x)^(x^2/(1 + x))*((2 + x)*cos(x)*log(cos(x)) - x*(1 + x)*sin(x))/((1 + x)^2*cos(x))
Compilar la expresión [src] 
           2                                                     
          x                                                      
        ----- //      2           \                  2          \
        x + 1 ||     x        2*x |                 x *sin(x)   |
(cos(x))     *||- -------- + -----|*log(cos(x)) - --------------|
              ||         2   1 + x|               (1 + x)*cos(x)|
              \\  (1 + x)         /                             /
(−x2sin⁡(x)(x+1)cos⁡(x)+(−x2(x+1)2+2xx+1)log⁡(cos⁡(x)))cos⁡x2x+1(x)\left(- \frac{x^{2} \sin{\left(x \right)}}{\left(x + 1\right) \cos{\left(x \right)}} + \left(- \frac{x^{2}}{\left(x + 1\right)^{2}} + \frac{2 x}{x + 1}\right) \log{\left(\cos{\left(x \right)} \right)}\right) \cos^{\frac{x^{2}}{x + 1}}{\left(x \right)} 
cos(x)^(x^2/(x + 1))*((-x^2/(1 + x)^2 + 2*x/(1 + x))*log(cos(x)) - x^2*sin(x)/((1 + x)*cos(x)))
    © Sr Examen – Калькулятор