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Simplificación de expresiones/ Descomposición en fracciones simples/ cos(x)/(3*x^2-4*x-1)+(4-6*x)*(sin(x)-1)/(3*x^2-4*x-1)^2+sinh(x)

¿Cómo vas a descomponer esta cos(x)/(3*x^2-4*x-1)+(4-6*x)*(sin(x)-1)/(3*x^2-4*x-1)^2+sinh(x) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
    cos(x)       (4 - 6*x)*(sin(x) - 1)          
-------------- + ---------------------- + sinh(x)
   2                               2             
3*x  - 4*x - 1     /   2          \              
                   \3*x  - 4*x - 1/
((4−6x)(sin⁡(x)−1)((3x2−4x)−1)2+cos⁡(x)(3x2−4x)−1)+sinh⁡(x)\left(\frac{\left(4 - 6 x\right) \left(\sin{\left(x \right)} - 1\right)}{\left(\left(3 x^{2} - 4 x\right) - 1\right)^{2}} + \frac{\cos{\left(x \right)}}{\left(3 x^{2} - 4 x\right) - 1}\right) + \sinh{\left(x \right)} 
cos(x)/(3*x^2 - 4*x - 1) + ((4 - 6*x)*(sin(x) - 1))/(3*x^2 - 4*x - 1)^2 + sinh(x)
Simplificación general [src] 
 /                                                                     2        \ 
 |                           /       2      \          /       2      \         | 
-\(-1 + sin(x))*(-4 + 6*x) + \1 - 3*x  + 4*x/*cos(x) - \1 - 3*x  + 4*x/ *sinh(x)/ 
----------------------------------------------------------------------------------
                                                2                                 
                                /       2      \                                  
                                \1 - 3*x  + 4*x/
−(6x−4)(sin⁡(x)−1)−(−3x2+4x+1)2sinh⁡(x)+(−3x2+4x+1)cos⁡(x)(−3x2+4x+1)2- \frac{\left(6 x - 4\right) \left(\sin{\left(x \right)} - 1\right) - \left(- 3 x^{2} + 4 x + 1\right)^{2} \sinh{\left(x \right)} + \left(- 3 x^{2} + 4 x + 1\right) \cos{\left(x \right)}}{\left(- 3 x^{2} + 4 x + 1\right)^{2}} 
-((-1 + sin(x))*(-4 + 6*x) + (1 - 3*x^2 + 4*x)*cos(x) - (1 - 3*x^2 + 4*x)^2*sinh(x))/(1 - 3*x^2 + 4*x)^2
Respuesta numérica [src] 
cos(x)/(-1.0 + 3.0*x^2 - 4.0*x) + 0.0625*(4.0 - 6.0*x)*(-1.0 + sin(x))/(-0.25 - x + 0.75*x^2)^2 + sinh(x)
cos(x)/(-1.0 + 3.0*x^2 - 4.0*x) + 0.0625*(4.0 - 6.0*x)*(-1.0 + sin(x))/(-0.25 - x + 0.75*x^2)^2 + sinh(x)
Denominador común [src] 
                                                            2                 
-4 - cos(x) + 4*sin(x) + 6*x - 6*x*sin(x) - 4*x*cos(x) + 3*x *cos(x)          
-------------------------------------------------------------------- + sinh(x)
                           3            4       2                             
                   1 - 24*x  + 8*x + 9*x  + 10*x
sinh⁡(x)+3x2cos⁡(x)−6xsin⁡(x)−4xcos⁡(x)+6x+4sin⁡(x)−cos⁡(x)−49x4−24x3+10x2+8x+1\sinh{\left(x \right)} + \frac{3 x^{2} \cos{\left(x \right)} - 6 x \sin{\left(x \right)} - 4 x \cos{\left(x \right)} + 6 x + 4 \sin{\left(x \right)} - \cos{\left(x \right)} - 4}{9 x^{4} - 24 x^{3} + 10 x^{2} + 8 x + 1} 
(-4 - cos(x) + 4*sin(x) + 6*x - 6*x*sin(x) - 4*x*cos(x) + 3*x^2*cos(x))/(1 - 24*x^3 + 8*x + 9*x^4 + 10*x^2) + sinh(x)
Potencias [src] 
     cos(x)       (-1 + sin(x))*(4 - 6*x)          
--------------- + ----------------------- + sinh(x)
              2                       2            
-1 - 4*x + 3*x       /              2\             
                     \-1 - 4*x + 3*x /
(4−6x)(sin⁡(x)−1)(3x2−4x−1)2+sinh⁡(x)+cos⁡(x)3x2−4x−1\frac{\left(4 - 6 x\right) \left(\sin{\left(x \right)} - 1\right)}{\left(3 x^{2} - 4 x - 1\right)^{2}} + \sinh{\left(x \right)} + \frac{\cos{\left(x \right)}}{3 x^{2} - 4 x - 1} 
   I*x    -I*x    /       /   -I*x    I*x\\                    
  e      e        |     I*\- e     + e   /|                    
  ---- + -----    |-1 - ------------------|*(4 - 6*x)          
   2       2      \             2         /                    
--------------- + ----------------------------------- + sinh(x)
              2                             2                  
-1 - 4*x + 3*x             /              2\                   
                           \-1 - 4*x + 3*x /
(4−6x)(−i(eix−e−ix)2−1)(3x2−4x−1)2+eix2+e−ix23x2−4x−1+sinh⁡(x)\frac{\left(4 - 6 x\right) \left(- \frac{i \left(e^{i x} - e^{- i x}\right)}{2} - 1\right)}{\left(3 x^{2} - 4 x - 1\right)^{2}} + \frac{\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}}{3 x^{2} - 4 x - 1} + \sinh{\left(x \right)} 
(exp(i*x)/2 + exp(-i*x)/2)/(-1 - 4*x + 3*x^2) + (-1 - i*(-exp(-i*x) + exp(i*x))/2)*(4 - 6*x)/(-1 - 4*x + 3*x^2)^2 + sinh(x)
Unión de expresiones racionales [src] 
                   2                                                                 
(-1 + x*(-4 + 3*x)) *sinh(x) + (-1 + x*(-4 + 3*x))*cos(x) + 2*(-1 + sin(x))*(2 - 3*x)
-------------------------------------------------------------------------------------
                                                    2                                
                                 (-1 + x*(-4 + 3*x))
2(2−3x)(sin⁡(x)−1)+(x(3x−4)−1)2sinh⁡(x)+(x(3x−4)−1)cos⁡(x)(x(3x−4)−1)2\frac{2 \left(2 - 3 x\right) \left(\sin{\left(x \right)} - 1\right) + \left(x \left(3 x - 4\right) - 1\right)^{2} \sinh{\left(x \right)} + \left(x \left(3 x - 4\right) - 1\right) \cos{\left(x \right)}}{\left(x \left(3 x - 4\right) - 1\right)^{2}} 
((-1 + x*(-4 + 3*x))^2*sinh(x) + (-1 + x*(-4 + 3*x))*cos(x) + 2*(-1 + sin(x))*(2 - 3*x))/(-1 + x*(-4 + 3*x))^2
Combinatoria [src] 
                                   3                                        2                           4               2                  
-4 - cos(x) + 4*sin(x) + 6*x - 24*x *sinh(x) - 6*x*sin(x) - 4*x*cos(x) + 3*x *cos(x) + 8*x*sinh(x) + 9*x *sinh(x) + 10*x *sinh(x) + sinh(x)
-------------------------------------------------------------------------------------------------------------------------------------------
                                                                              2                                                            
                                                             /              2\                                                             
                                                             \-1 - 4*x + 3*x /
9x4sinh⁡(x)−24x3sinh⁡(x)+3x2cos⁡(x)+10x2sinh⁡(x)−6xsin⁡(x)−4xcos⁡(x)+8xsinh⁡(x)+6x+4sin⁡(x)−cos⁡(x)+sinh⁡(x)−4(3x2−4x−1)2\frac{9 x^{4} \sinh{\left(x \right)} - 24 x^{3} \sinh{\left(x \right)} + 3 x^{2} \cos{\left(x \right)} + 10 x^{2} \sinh{\left(x \right)} - 6 x \sin{\left(x \right)} - 4 x \cos{\left(x \right)} + 8 x \sinh{\left(x \right)} + 6 x + 4 \sin{\left(x \right)} - \cos{\left(x \right)} + \sinh{\left(x \right)} - 4}{\left(3 x^{2} - 4 x - 1\right)^{2}} 
(-4 - cos(x) + 4*sin(x) + 6*x - 24*x^3*sinh(x) - 6*x*sin(x) - 4*x*cos(x) + 3*x^2*cos(x) + 8*x*sinh(x) + 9*x^4*sinh(x) + 10*x^2*sinh(x) + sinh(x))/(-1 - 4*x + 3*x^2)^2
Compilar la expresión [src] 
     cos(x)       (-1 + sin(x))*(4 - 6*x)          
--------------- + ----------------------- + sinh(x)
              2                       2            
-1 - 4*x + 3*x       /              2\             
                     \-1 - 4*x + 3*x /
(4−6x)(sin⁡(x)−1)(3x2−4x−1)2+sinh⁡(x)+cos⁡(x)3x2−4x−1\frac{\left(4 - 6 x\right) \left(\sin{\left(x \right)} - 1\right)}{\left(3 x^{2} - 4 x - 1\right)^{2}} + \sinh{\left(x \right)} + \frac{\cos{\left(x \right)}}{3 x^{2} - 4 x - 1} 
cos(x)/(-1 - 4*x + 3*x^2) + (-1 + sin(x))*(4 - 6*x)/(-1 - 4*x + 3*x^2)^2 + sinh(x)
Denominador racional [src] 
                 2                           3                                                    
/              2\           /              2\                                    /              2\
\-1 - 4*x + 3*x / *cos(x) + \-1 - 4*x + 3*x / *sinh(x) + (-1 + sin(x))*(4 - 6*x)*\-1 - 4*x + 3*x /
--------------------------------------------------------------------------------------------------
                                                         3                                        
                                        /              2\                                         
                                        \-1 - 4*x + 3*x /
(4−6x)(sin⁡(x)−1)(3x2−4x−1)+(3x2−4x−1)3sinh⁡(x)+(3x2−4x−1)2cos⁡(x)(3x2−4x−1)3\frac{\left(4 - 6 x\right) \left(\sin{\left(x \right)} - 1\right) \left(3 x^{2} - 4 x - 1\right) + \left(3 x^{2} - 4 x - 1\right)^{3} \sinh{\left(x \right)} + \left(3 x^{2} - 4 x - 1\right)^{2} \cos{\left(x \right)}}{\left(3 x^{2} - 4 x - 1\right)^{3}} 
((-1 - 4*x + 3*x^2)^2*cos(x) + (-1 - 4*x + 3*x^2)^3*sinh(x) + (-1 + sin(x))*(4 - 6*x)*(-1 - 4*x + 3*x^2))/(-1 - 4*x + 3*x^2)^3
Abrimos la expresión [src] 
                4                      cos(x)                  4*sin(x)                           6*x                           6*x*sin(x)                    
- ------------------------------ + -------------- + ------------------------------ + ------------------------------ - ------------------------------ + sinh(x)
          3            4       2      2                     3            4       2           3            4       2           3            4       2          
  1 - 24*x  + 8*x + 9*x  + 10*x    3*x  - 4*x - 1   1 - 24*x  + 8*x + 9*x  + 10*x    1 - 24*x  + 8*x + 9*x  + 10*x    1 - 24*x  + 8*x + 9*x  + 10*x
−6xsin⁡(x)9x4−24x3+10x2+8x+1+6x9x4−24x3+10x2+8x+1+sinh⁡(x)+4sin⁡(x)9x4−24x3+10x2+8x+1−49x4−24x3+10x2+8x+1+cos⁡(x)(3x2−4x)−1- \frac{6 x \sin{\left(x \right)}}{9 x^{4} - 24 x^{3} + 10 x^{2} + 8 x + 1} + \frac{6 x}{9 x^{4} - 24 x^{3} + 10 x^{2} + 8 x + 1} + \sinh{\left(x \right)} + \frac{4 \sin{\left(x \right)}}{9 x^{4} - 24 x^{3} + 10 x^{2} + 8 x + 1} - \frac{4}{9 x^{4} - 24 x^{3} + 10 x^{2} + 8 x + 1} + \frac{\cos{\left(x \right)}}{\left(3 x^{2} - 4 x\right) - 1} 
-4/(1 - 24*x^3 + 8*x + 9*x^4 + 10*x^2) + cos(x)/(3*x^2 - 4*x - 1) + 4*sin(x)/(1 - 24*x^3 + 8*x + 9*x^4 + 10*x^2) + 6*x/(1 - 24*x^3 + 8*x + 9*x^4 + 10*x^2) - 6*x*sin(x)/(1 - 24*x^3 + 8*x + 9*x^4 + 10*x^2) + sinh(x)
Parte trigonométrica [src] 
                            /          1     \                     
                            |-1 + -----------|*(-4 + 6*x)          
                            |        /    pi\|                     
                            |     sec|x - --||                     
             1              \        \    2 //                     
- ----------------------- - ----------------------------- + sinh(x)
  /       2      \                                2                
  \1 - 3*x  + 4*x/*sec(x)         /       2      \                 
                                  \1 - 3*x  + 4*x/
−(−1+1sec⁡(x−π2))(6x−4)(−3x2+4x+1)2+sinh⁡(x)−1(−3x2+4x+1)sec⁡(x)- \frac{\left(-1 + \frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}\right) \left(6 x - 4\right)}{\left(- 3 x^{2} + 4 x + 1\right)^{2}} + \sinh{\left(x \right)} - \frac{1}{\left(- 3 x^{2} + 4 x + 1\right) \sec{\left(x \right)}} 
     /    pi\                                      
  sin|x + --|                                      
     \    2 /     (-1 + sin(x))*(4 - 6*x)          
--------------- + ----------------------- + sinh(x)
              2                       2            
-1 - 4*x + 3*x       /              2\             
                     \-1 - 4*x + 3*x /
(4−6x)(sin⁡(x)−1)(3x2−4x−1)2+sinh⁡(x)+sin⁡(x+π2)3x2−4x−1\frac{\left(4 - 6 x\right) \left(\sin{\left(x \right)} - 1\right)}{\left(3 x^{2} - 4 x - 1\right)^{2}} + \sinh{\left(x \right)} + \frac{\sin{\left(x + \frac{\pi}{2} \right)}}{3 x^{2} - 4 x - 1} 
                   /        /    pi\\                     
                   |-1 + cos|x - --||*(-4 + 6*x)          
      cos(x)       \        \    2 //                     
- -------------- - ----------------------------- + sinh(x)
         2                               2                
  1 - 3*x  + 4*x         /       2      \                 
                         \1 - 3*x  + 4*x/
−(6x−4)(cos⁡(x−π2)−1)(−3x2+4x+1)2+sinh⁡(x)−cos⁡(x)−3x2+4x+1- \frac{\left(6 x - 4\right) \left(\cos{\left(x - \frac{\pi}{2} \right)} - 1\right)}{\left(- 3 x^{2} + 4 x + 1\right)^{2}} + \sinh{\left(x \right)} - \frac{\cos{\left(x \right)}}{- 3 x^{2} + 4 x + 1} 
                           /       1   \                    
                           |-1 + ------|*(4 - 6*x)          
           1               \     csc(x)/                    
------------------------ + ----------------------- + sinh(x)
/              2\                              2            
\-1 - 4*x + 3*x /*sec(x)      /              2\             
                              \-1 - 4*x + 3*x /
(−1+1csc⁡(x))(4−6x)(3x2−4x−1)2+sinh⁡(x)+1(3x2−4x−1)sec⁡(x)\frac{\left(-1 + \frac{1}{\csc{\left(x \right)}}\right) \left(4 - 6 x\right)}{\left(3 x^{2} - 4 x - 1\right)^{2}} + \sinh{\left(x \right)} + \frac{1}{\left(3 x^{2} - 4 x - 1\right) \sec{\left(x \right)}} 
                                 /       1   \                     
                                 |-1 + ------|*(-4 + 6*x)          
               1                 \     csc(x)/                     
- ---------------------------- - ------------------------ + sinh(x)
  /       2      \    /pi    \                      2              
  \1 - 3*x  + 4*x/*csc|-- - x|      /       2      \               
                      \2     /      \1 - 3*x  + 4*x/
−(−1+1csc⁡(x))(6x−4)(−3x2+4x+1)2+sinh⁡(x)−1(−3x2+4x+1)csc⁡(−x+π2)- \frac{\left(-1 + \frac{1}{\csc{\left(x \right)}}\right) \left(6 x - 4\right)}{\left(- 3 x^{2} + 4 x + 1\right)^{2}} + \sinh{\left(x \right)} - \frac{1}{\left(- 3 x^{2} + 4 x + 1\right) \csc{\left(- x + \frac{\pi}{2} \right)}} 
                                /       1   \                    
                                |-1 + ------|*(4 - 6*x)          
              1                 \     csc(x)/                    
----------------------------- + ----------------------- + sinh(x)
/              2\    /pi    \                       2            
\-1 - 4*x + 3*x /*csc|-- - x|      /              2\             
                     \2     /      \-1 - 4*x + 3*x /
(−1+1csc⁡(x))(4−6x)(3x2−4x−1)2+sinh⁡(x)+1(3x2−4x−1)csc⁡(−x+π2)\frac{\left(-1 + \frac{1}{\csc{\left(x \right)}}\right) \left(4 - 6 x\right)}{\left(3 x^{2} - 4 x - 1\right)^{2}} + \sinh{\left(x \right)} + \frac{1}{\left(3 x^{2} - 4 x - 1\right) \csc{\left(- x + \frac{\pi}{2} \right)}} 
                           /          1     \                    
                           |-1 + -----------|*(4 - 6*x)          
                           |        /    pi\|                    
                           |     sec|x - --||                    
           1               \        \    2 //                    
------------------------ + ---------------------------- + sinh(x)
/              2\                                2               
\-1 - 4*x + 3*x /*sec(x)        /              2\                
                                \-1 - 4*x + 3*x /
(−1+1sec⁡(x−π2))(4−6x)(3x2−4x−1)2+sinh⁡(x)+1(3x2−4x−1)sec⁡(x)\frac{\left(-1 + \frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}\right) \left(4 - 6 x\right)}{\left(3 x^{2} - 4 x - 1\right)^{2}} + \sinh{\left(x \right)} + \frac{1}{\left(3 x^{2} - 4 x - 1\right) \sec{\left(x \right)}} 
      cos(x)       (-1 + sin(x))*(-4 + 6*x)          
- -------------- - ------------------------ + sinh(x)
         2                            2              
  1 - 3*x  + 4*x      /       2      \               
                      \1 - 3*x  + 4*x/
−(6x−4)(sin⁡(x)−1)(−3x2+4x+1)2+sinh⁡(x)−cos⁡(x)−3x2+4x+1- \frac{\left(6 x - 4\right) \left(\sin{\left(x \right)} - 1\right)}{\left(- 3 x^{2} + 4 x + 1\right)^{2}} + \sinh{\left(x \right)} - \frac{\cos{\left(x \right)}}{- 3 x^{2} + 4 x + 1} 
     cos(x)       (-1 + sin(x))*(4 - 6*x)          
--------------- + ----------------------- + sinh(x)
              2                       2            
-1 - 4*x + 3*x       /              2\             
                     \-1 - 4*x + 3*x /
(4−6x)(sin⁡(x)−1)(3x2−4x−1)2+sinh⁡(x)+cos⁡(x)3x2−4x−1\frac{\left(4 - 6 x\right) \left(\sin{\left(x \right)} - 1\right)}{\left(3 x^{2} - 4 x - 1\right)^{2}} + \sinh{\left(x \right)} + \frac{\cos{\left(x \right)}}{3 x^{2} - 4 x - 1} 
                                   /            /x\ \                     
                                   |       2*tan|-| |                     
                                   |            \2/ |                     
                                   |-1 + -----------|*(-4 + 6*x)          
                  2/x\             |            2/x\|                     
           1 - tan |-|             |     1 + tan |-||                     
                   \2/             \             \2//                     
- ------------------------------ - ----------------------------- + sinh(x)
  /       2/x\\ /       2      \                         2                
  |1 + tan |-||*\1 - 3*x  + 4*x/         /       2      \                 
  \        \2//                          \1 - 3*x  + 4*x/
−(−1+2tan⁡(x2)tan⁡2(x2)+1)(6x−4)(−3x2+4x+1)2−1−tan⁡2(x2)(tan⁡2(x2)+1)(−3x2+4x+1)+sinh⁡(x)- \frac{\left(-1 + \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(6 x - 4\right)}{\left(- 3 x^{2} + 4 x + 1\right)^{2}} - \frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right) \left(- 3 x^{2} + 4 x + 1\right)} + \sinh{\left(x \right)} 
                  /        /    pi\\                    
                  |-1 + cos|x - --||*(4 - 6*x)          
     cos(x)       \        \    2 //                    
--------------- + ---------------------------- + sinh(x)
              2                         2               
-1 - 4*x + 3*x         /              2\                
                       \-1 - 4*x + 3*x /
(4−6x)(cos⁡(x−π2)−1)(3x2−4x−1)2+sinh⁡(x)+cos⁡(x)3x2−4x−1\frac{\left(4 - 6 x\right) \left(\cos{\left(x - \frac{\pi}{2} \right)} - 1\right)}{\left(3 x^{2} - 4 x - 1\right)^{2}} + \sinh{\left(x \right)} + \frac{\cos{\left(x \right)}}{3 x^{2} - 4 x - 1} 
      /    pi\                                       
   sin|x + --|                                       
      \    2 /     (-1 + sin(x))*(-4 + 6*x)          
- -------------- - ------------------------ + sinh(x)
         2                            2              
  1 - 3*x  + 4*x      /       2      \               
                      \1 - 3*x  + 4*x/
−(6x−4)(sin⁡(x)−1)(−3x2+4x+1)2+sinh⁡(x)−sin⁡(x+π2)−3x2+4x+1- \frac{\left(6 x - 4\right) \left(\sin{\left(x \right)} - 1\right)}{\left(- 3 x^{2} + 4 x + 1\right)^{2}} + \sinh{\left(x \right)} - \frac{\sin{\left(x + \frac{\pi}{2} \right)}}{- 3 x^{2} + 4 x + 1} 
                                  /            /x\ \                    
                                  |       2*cot|-| |                    
                                  |            \2/ |                    
                                  |-1 + -----------|*(4 - 6*x)          
                  2/x\            |            2/x\|                    
          -1 + cot |-|            |     1 + cot |-||                    
                   \2/            \             \2//                    
------------------------------- + ---------------------------- + sinh(x)
/       2/x\\ /              2\                         2               
|1 + cot |-||*\-1 - 4*x + 3*x /        /              2\                
\        \2//                          \-1 - 4*x + 3*x /
(−1+2cot⁡(x2)cot⁡2(x2)+1)(4−6x)(3x2−4x−1)2+cot⁡2(x2)−1(cot⁡2(x2)+1)(3x2−4x−1)+sinh⁡(x)\frac{\left(-1 + \frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(4 - 6 x\right)}{\left(3 x^{2} - 4 x - 1\right)^{2}} + \frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \left(3 x^{2} - 4 x - 1\right)} + \sinh{\left(x \right)} 
                                   /            /x\ \                     
                                   |       2*cot|-| |                     
                                   |            \2/ |                     
                                   |-1 + -----------|*(-4 + 6*x)          
                   2/x\            |            2/x\|                     
           -1 + cot |-|            |     1 + cot |-||                     
                    \2/            \             \2//                     
- ------------------------------ - ----------------------------- + sinh(x)
  /       2/x\\ /       2      \                         2                
  |1 + cot |-||*\1 - 3*x  + 4*x/         /       2      \                 
  \        \2//                          \1 - 3*x  + 4*x/
−(−1+2cot⁡(x2)cot⁡2(x2)+1)(6x−4)(−3x2+4x+1)2−cot⁡2(x2)−1(cot⁡2(x2)+1)(−3x2+4x+1)+sinh⁡(x)- \frac{\left(-1 + \frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(6 x - 4\right)}{\left(- 3 x^{2} + 4 x + 1\right)^{2}} - \frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \left(- 3 x^{2} + 4 x + 1\right)} + \sinh{\left(x \right)} 
                                  /            /x\ \                    
                                  |       2*tan|-| |                    
                                  |            \2/ |                    
                                  |-1 + -----------|*(4 - 6*x)          
                 2/x\             |            2/x\|                    
          1 - tan |-|             |     1 + tan |-||                    
                  \2/             \             \2//                    
------------------------------- + ---------------------------- + sinh(x)
/       2/x\\ /              2\                         2               
|1 + tan |-||*\-1 - 4*x + 3*x /        /              2\                
\        \2//                          \-1 - 4*x + 3*x /
(−1+2tan⁡(x2)tan⁡2(x2)+1)(4−6x)(3x2−4x−1)2+1−tan⁡2(x2)(tan⁡2(x2)+1)(3x2−4x−1)+sinh⁡(x)\frac{\left(-1 + \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(4 - 6 x\right)}{\left(3 x^{2} - 4 x - 1\right)^{2}} + \frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right) \left(3 x^{2} - 4 x - 1\right)} + \sinh{\left(x \right)} 
(1 - tan(x/2)^2)/((1 + tan(x/2)^2)*(-1 - 4*x + 3*x^2)) + (-1 + 2*tan(x/2)/(1 + tan(x/2)^2))*(4 - 6*x)/(-1 - 4*x + 3*x^2)^2 + sinh(x)
    © Sr Examen – Калькулятор