Sr Examen

Otras calculadoras

Simplificación de expresiones/ Descomposición en fracciones simples/ sin((6*k+1)*x)/(2*(1+6*k))+sin((1-6*k)*x)/(2*(1-6*k))

¿Cómo vas a descomponer esta sin((6*k+1)*x)/(2*(1+6*k))+sin((1-6*k)*x)/(2*(1-6*k)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
sin((6*k + 1)*x)   sin((1 - 6*k)*x)
---------------- + ----------------
  2*(1 + 6*k)        2*(1 - 6*k)
sin⁡(x(6k+1))2(6k+1)+sin⁡(x(1−6k))2(1−6k)\frac{\sin{\left(x \left(6 k + 1\right) \right)}}{2 \left(6 k + 1\right)} + \frac{\sin{\left(x \left(1 - 6 k\right) \right)}}{2 \left(1 - 6 k\right)} 
sin((6*k + 1)*x)/((2*(1 + 6*k))) + sin((1 - 6*k)*x)/((2*(1 - 6*k)))
Simplificación general [src] 
(1 + 6*k)*sin(x*(-1 + 6*k)) + (-1 + 6*k)*sin(x + 6*k*x)
-------------------------------------------------------
                 2*(1 + 6*k)*(-1 + 6*k)
(6k−1)sin⁡(6kx+x)+(6k+1)sin⁡(x(6k−1))2(6k−1)(6k+1)\frac{\left(6 k - 1\right) \sin{\left(6 k x + x \right)} + \left(6 k + 1\right) \sin{\left(x \left(6 k - 1\right) \right)}}{2 \left(6 k - 1\right) \left(6 k + 1\right)} 
((1 + 6*k)*sin(x*(-1 + 6*k)) + (-1 + 6*k)*sin(x + 6*k*x))/(2*(1 + 6*k)*(-1 + 6*k))
Unión de expresiones racionales [src] 
(1 - 6*k)*sin(x*(1 + 6*k)) + (1 + 6*k)*sin(x*(1 - 6*k))
-------------------------------------------------------
                 2*(1 - 6*k)*(1 + 6*k)
(1−6k)sin⁡(x(6k+1))+(6k+1)sin⁡(x(1−6k))2(1−6k)(6k+1)\frac{\left(1 - 6 k\right) \sin{\left(x \left(6 k + 1\right) \right)} + \left(6 k + 1\right) \sin{\left(x \left(1 - 6 k\right) \right)}}{2 \left(1 - 6 k\right) \left(6 k + 1\right)} 
((1 - 6*k)*sin(x*(1 + 6*k)) + (1 + 6*k)*sin(x*(1 - 6*k)))/(2*(1 - 6*k)*(1 + 6*k))
Denominador racional [src] 
-2*sin(x + 6*k*x) + 2*sin(-x + 6*k*x) + 12*k*sin(x + 6*k*x) + 12*k*sin(-x + 6*k*x)
----------------------------------------------------------------------------------
                              (-2 + 12*k)*(2 + 12*k)
12ksin⁡(6kx−x)+12ksin⁡(6kx+x)+2sin⁡(6kx−x)−2sin⁡(6kx+x)(12k−2)(12k+2)\frac{12 k \sin{\left(6 k x - x \right)} + 12 k \sin{\left(6 k x + x \right)} + 2 \sin{\left(6 k x - x \right)} - 2 \sin{\left(6 k x + x \right)}}{\left(12 k - 2\right) \left(12 k + 2\right)} 
(-2*sin(x + 6*k*x) + 2*sin(-x + 6*k*x) + 12*k*sin(x + 6*k*x) + 12*k*sin(-x + 6*k*x))/((-2 + 12*k)*(2 + 12*k))
Denominador común [src] 
-sin(x + 6*k*x) + 6*k*sin(x + 6*k*x) + 6*k*sin(-x + 6*k*x) + sin(-x + 6*k*x)
----------------------------------------------------------------------------
                                          2                                 
                                 -2 + 72*k
6ksin⁡(6kx−x)+6ksin⁡(6kx+x)+sin⁡(6kx−x)−sin⁡(6kx+x)72k2−2\frac{6 k \sin{\left(6 k x - x \right)} + 6 k \sin{\left(6 k x + x \right)} + \sin{\left(6 k x - x \right)} - \sin{\left(6 k x + x \right)}}{72 k^{2} - 2} 
(-sin(x + 6*k*x) + 6*k*sin(x + 6*k*x) + 6*k*sin(-x + 6*k*x) + sin(-x + 6*k*x))/(-2 + 72*k^2)
Compilar la expresión [src] 
sin((1 - 6*k)*x)   sin((6*k + 1)*x)
---------------- + ----------------
    2 - 12*k           2 + 12*k
sin⁡(x(6k+1))12k+2+sin⁡(x(1−6k))2−12k\frac{\sin{\left(x \left(6 k + 1\right) \right)}}{12 k + 2} + \frac{\sin{\left(x \left(1 - 6 k\right) \right)}}{2 - 12 k} 
sin((1 - 6*k)*x)/(2 - 12*k) + sin((6*k + 1)*x)/(2 + 12*k)
Abrimos la expresión [src] 
                              4                     4                     2                     2                     6                     6                     5                              3                                                                                        3                              5                     
   sin(x)     sin(x)    48*cos (k*x)*sin(x)   48*cos (k*x)*sin(x)   18*cos (k*x)*sin(x)   18*cos (k*x)*sin(x)   32*cos (k*x)*sin(x)   32*cos (k*x)*sin(x)   32*sin (k*x)*cos(x)*cos(k*x)   32*sin (k*x)*cos(x)*cos(k*x)   6*cos(x)*cos(k*x)*sin(k*x)   6*cos(x)*cos(k*x)*sin(k*x)   32*sin (k*x)*cos(x)*cos(k*x)   32*sin (k*x)*cos(x)*cos(k*x)
- -------- - -------- - ------------------- - ------------------- + ------------------- + ------------------- + ------------------- + ------------------- - ---------------------------- - ---------------------------- - -------------------------- + -------------------------- + ---------------------------- + ----------------------------
  2 - 12*k   2 + 12*k         2 - 12*k              2 + 12*k              2 - 12*k              2 + 12*k              2 - 12*k              2 + 12*k                  2 - 12*k                       2 + 12*k                      2 - 12*k                     2 + 12*k                      2 - 12*k                       2 + 12*k
32sin⁡(x)cos⁡6(kx)12k+2−48sin⁡(x)cos⁡4(kx)12k+2+18sin⁡(x)cos⁡2(kx)12k+2−sin⁡(x)12k+2+32sin⁡5(kx)cos⁡(x)cos⁡(kx)12k+2−32sin⁡3(kx)cos⁡(x)cos⁡(kx)12k+2+6sin⁡(kx)cos⁡(x)cos⁡(kx)12k+2+32sin⁡(x)cos⁡6(kx)2−12k−48sin⁡(x)cos⁡4(kx)2−12k+18sin⁡(x)cos⁡2(kx)2−12k−sin⁡(x)2−12k−32sin⁡5(kx)cos⁡(x)cos⁡(kx)2−12k+32sin⁡3(kx)cos⁡(x)cos⁡(kx)2−12k−6sin⁡(kx)cos⁡(x)cos⁡(kx)2−12k\frac{32 \sin{\left(x \right)} \cos^{6}{\left(k x \right)}}{12 k + 2} - \frac{48 \sin{\left(x \right)} \cos^{4}{\left(k x \right)}}{12 k + 2} + \frac{18 \sin{\left(x \right)} \cos^{2}{\left(k x \right)}}{12 k + 2} - \frac{\sin{\left(x \right)}}{12 k + 2} + \frac{32 \sin^{5}{\left(k x \right)} \cos{\left(x \right)} \cos{\left(k x \right)}}{12 k + 2} - \frac{32 \sin^{3}{\left(k x \right)} \cos{\left(x \right)} \cos{\left(k x \right)}}{12 k + 2} + \frac{6 \sin{\left(k x \right)} \cos{\left(x \right)} \cos{\left(k x \right)}}{12 k + 2} + \frac{32 \sin{\left(x \right)} \cos^{6}{\left(k x \right)}}{2 - 12 k} - \frac{48 \sin{\left(x \right)} \cos^{4}{\left(k x \right)}}{2 - 12 k} + \frac{18 \sin{\left(x \right)} \cos^{2}{\left(k x \right)}}{2 - 12 k} - \frac{\sin{\left(x \right)}}{2 - 12 k} - \frac{32 \sin^{5}{\left(k x \right)} \cos{\left(x \right)} \cos{\left(k x \right)}}{2 - 12 k} + \frac{32 \sin^{3}{\left(k x \right)} \cos{\left(x \right)} \cos{\left(k x \right)}}{2 - 12 k} - \frac{6 \sin{\left(k x \right)} \cos{\left(x \right)} \cos{\left(k x \right)}}{2 - 12 k} 
-sin(x)/(2 - 12*k) - sin(x)/(2 + 12*k) - 48*cos(k*x)^4*sin(x)/(2 - 12*k) - 48*cos(k*x)^4*sin(x)/(2 + 12*k) + 18*cos(k*x)^2*sin(x)/(2 - 12*k) + 18*cos(k*x)^2*sin(x)/(2 + 12*k) + 32*cos(k*x)^6*sin(x)/(2 - 12*k) + 32*cos(k*x)^6*sin(x)/(2 + 12*k) - 32*sin(k*x)^5*cos(x)*cos(k*x)/(2 - 12*k) - 32*sin(k*x)^3*cos(x)*cos(k*x)/(2 + 12*k) - 6*cos(x)*cos(k*x)*sin(k*x)/(2 - 12*k) + 6*cos(x)*cos(k*x)*sin(k*x)/(2 + 12*k) + 32*sin(k*x)^3*cos(x)*cos(k*x)/(2 - 12*k) + 32*sin(k*x)^5*cos(x)*cos(k*x)/(2 + 12*k)
Respuesta numérica [src] 
sin((6*k + 1)*x)/(2.0 + 12.0*k) + sin((1 - 6*k)*x)/(2.0 - 12.0*k)
sin((6*k + 1)*x)/(2.0 + 12.0*k) + sin((1 - 6*k)*x)/(2.0 - 12.0*k)
Parte trigonométrica [src] 
               1                                 1               
-------------------------------- + ------------------------------
              /pi              \                 /    pi        \
(2 - 12*k)*sec|-- - x*(1 - 6*k)|   (2 + 12*k)*sec|x - -- + 6*k*x|
              \2               /                 \    2         /
1(12k+2)sec⁡(6kx+x−π2)+1(2−12k)sec⁡(−x(1−6k)+π2)\frac{1}{\left(12 k + 2\right) \sec{\left(6 k x + x - \frac{\pi}{2} \right)}} + \frac{1}{\left(2 - 12 k\right) \sec{\left(- x \left(1 - 6 k\right) + \frac{\pi}{2} \right)}} 
   /  pi              \      /    pi        \
cos|- -- + x*(1 - 6*k)|   cos|x - -- + 6*k*x|
   \  2               /      \    2         /
----------------------- + -------------------
        2 - 12*k                2 + 12*k
cos⁡(6kx+x−π2)12k+2+cos⁡(x(1−6k)−π2)2−12k\frac{\cos{\left(6 k x + x - \frac{\pi}{2} \right)}}{12 k + 2} + \frac{\cos{\left(x \left(1 - 6 k\right) - \frac{\pi}{2} \right)}}{2 - 12 k} 
   /  pi              \      /  pi              \
cos|- -- + x*(1 - 6*k)|   cos|- -- + x*(1 + 6*k)|
   \  2               /      \  2               /
----------------------- + -----------------------
        2 - 12*k                  2 + 12*k
cos⁡(x(6k+1)−π2)12k+2+cos⁡(x(1−6k)−π2)2−12k\frac{\cos{\left(x \left(6 k + 1\right) - \frac{\pi}{2} \right)}}{12 k + 2} + \frac{\cos{\left(x \left(1 - 6 k\right) - \frac{\pi}{2} \right)}}{2 - 12 k} 
sin(x*(1 - 6*k))   sin(x*(1 + 6*k))
---------------- + ----------------
    2 - 12*k           2 + 12*k
sin⁡(x(6k+1))12k+2+sin⁡(x(1−6k))2−12k\frac{\sin{\left(x \left(6 k + 1\right) \right)}}{12 k + 2} + \frac{\sin{\left(x \left(1 - 6 k\right) \right)}}{2 - 12 k} 
   /    pi        \      /  pi               \
cos|x - -- + 6*k*x|   cos|- -- + x*(-1 + 6*k)|
   \    2         /      \  2                /
------------------- - ------------------------
      2 + 12*k                2 - 12*k
cos⁡(6kx+x−π2)12k+2−cos⁡(x(6k−1)−π2)2−12k\frac{\cos{\left(6 k x + x - \frac{\pi}{2} \right)}}{12 k + 2} - \frac{\cos{\left(x \left(6 k - 1\right) - \frac{\pi}{2} \right)}}{2 - 12 k} 
sin(x*(1 - 6*k))   sin(x + 6*k*x)
---------------- + --------------
    2 - 12*k          2 + 12*k
sin⁡(6kx+x)12k+2+sin⁡(x(1−6k))2−12k\frac{\sin{\left(6 k x + x \right)}}{12 k + 2} + \frac{\sin{\left(x \left(1 - 6 k\right) \right)}}{2 - 12 k} 
                1                                  1               
---------------------------------- + ------------------------------
              /  pi              \                 /    pi        \
(2 - 12*k)*sec|- -- + x*(1 - 6*k)|   (2 + 12*k)*sec|x - -- + 6*k*x|
              \  2               /                 \    2         /
1(12k+2)sec⁡(6kx+x−π2)+1(2−12k)sec⁡(x(1−6k)−π2)\frac{1}{\left(12 k + 2\right) \sec{\left(6 k x + x - \frac{\pi}{2} \right)}} + \frac{1}{\left(2 - 12 k\right) \sec{\left(x \left(1 - 6 k\right) - \frac{\pi}{2} \right)}} 
            1                            1              
------------------------- - ----------------------------
(2 + 12*k)*csc(x + 6*k*x)   (2 - 12*k)*csc(x*(-1 + 6*k))
1(12k+2)csc⁡(6kx+x)−1(2−12k)csc⁡(x(6k−1))\frac{1}{\left(12 k + 2\right) \csc{\left(6 k x + x \right)}} - \frac{1}{\left(2 - 12 k\right) \csc{\left(x \left(6 k - 1\right) \right)}} 
              1                                   1                 
------------------------------ - -----------------------------------
              /    pi        \                 /  pi               \
(2 + 12*k)*sec|x - -- + 6*k*x|   (2 - 12*k)*sec|- -- + x*(-1 + 6*k)|
              \    2         /                 \  2                /
1(12k+2)sec⁡(6kx+x−π2)−1(2−12k)sec⁡(x(6k−1)−π2)\frac{1}{\left(12 k + 2\right) \sec{\left(6 k x + x - \frac{\pi}{2} \right)}} - \frac{1}{\left(2 - 12 k\right) \sec{\left(x \left(6 k - 1\right) - \frac{\pi}{2} \right)}} 
             1                            1            
--------------------------- + -------------------------
(2 - 12*k)*csc(x*(1 - 6*k))   (2 + 12*k)*csc(x + 6*k*x)
1(12k+2)csc⁡(6kx+x)+1(2−12k)csc⁡(x(1−6k))\frac{1}{\left(12 k + 2\right) \csc{\left(6 k x + x \right)}} + \frac{1}{\left(2 - 12 k\right) \csc{\left(x \left(1 - 6 k\right) \right)}} 
             /x*(1 - 6*k)\                        /x        \        
        2*cot|-----------|                   2*cot|- + 3*k*x|        
             \     2     /                        \2        /        
---------------------------------- + --------------------------------
/       2/x*(1 - 6*k)\\              /       2/x        \\           
|1 + cot |-----------||*(2 - 12*k)   |1 + cot |- + 3*k*x||*(2 + 12*k)
\        \     2     //              \        \2        //
2cot⁡(3kx+x2)(12k+2)(cot⁡2(3kx+x2)+1)+2cot⁡(x(1−6k)2)(2−12k)(cot⁡2(x(1−6k)2)+1)\frac{2 \cot{\left(3 k x + \frac{x}{2} \right)}}{\left(12 k + 2\right) \left(\cot^{2}{\left(3 k x + \frac{x}{2} \right)} + 1\right)} + \frac{2 \cot{\left(\frac{x \left(1 - 6 k\right)}{2} \right)}}{\left(2 - 12 k\right) \left(\cot^{2}{\left(\frac{x \left(1 - 6 k\right)}{2} \right)} + 1\right)} 
             /x*(1 - 6*k)\                        /x*(1 + 6*k)\        
        2*cot|-----------|                   2*cot|-----------|        
             \     2     /                        \     2     /        
---------------------------------- + ----------------------------------
/       2/x*(1 - 6*k)\\              /       2/x*(1 + 6*k)\\           
|1 + cot |-----------||*(2 - 12*k)   |1 + cot |-----------||*(2 + 12*k)
\        \     2     //              \        \     2     //
2cot⁡(x(6k+1)2)(12k+2)(cot⁡2(x(6k+1)2)+1)+2cot⁡(x(1−6k)2)(2−12k)(cot⁡2(x(1−6k)2)+1)\frac{2 \cot{\left(\frac{x \left(6 k + 1\right)}{2} \right)}}{\left(12 k + 2\right) \left(\cot^{2}{\left(\frac{x \left(6 k + 1\right)}{2} \right)} + 1\right)} + \frac{2 \cot{\left(\frac{x \left(1 - 6 k\right)}{2} \right)}}{\left(2 - 12 k\right) \left(\cot^{2}{\left(\frac{x \left(1 - 6 k\right)}{2} \right)} + 1\right)} 
             1                             1             
--------------------------- + ---------------------------
(2 - 12*k)*csc(x*(1 - 6*k))   (2 + 12*k)*csc(x*(1 + 6*k))
1(12k+2)csc⁡(x(6k+1))+1(2−12k)csc⁡(x(1−6k))\frac{1}{\left(12 k + 2\right) \csc{\left(x \left(6 k + 1\right) \right)}} + \frac{1}{\left(2 - 12 k\right) \csc{\left(x \left(1 - 6 k\right) \right)}} 
             1                sin(x + 6*k*x)
--------------------------- + --------------
(2 - 12*k)*csc(x*(1 - 6*k))      2 + 12*k
sin⁡(6kx+x)12k+2+1(2−12k)csc⁡(x(1−6k))\frac{\sin{\left(6 k x + x \right)}}{12 k + 2} + \frac{1}{\left(2 - 12 k\right) \csc{\left(x \left(1 - 6 k\right) \right)}} 
sin(x + 6*k*x)   sin(x*(-1 + 6*k))
-------------- - -----------------
   2 + 12*k           2 - 12*k
sin⁡(6kx+x)12k+2−sin⁡(x(6k−1))2−12k\frac{\sin{\left(6 k x + x \right)}}{12 k + 2} - \frac{\sin{\left(x \left(6 k - 1\right) \right)}}{2 - 12 k} 
             /x*(1 - 6*k)\                        /x        \        
        2*tan|-----------|                   2*tan|- + 3*k*x|        
             \     2     /                        \2        /        
---------------------------------- + --------------------------------
/       2/x*(1 - 6*k)\\              /       2/x        \\           
|1 + tan |-----------||*(2 - 12*k)   |1 + tan |- + 3*k*x||*(2 + 12*k)
\        \     2     //              \        \2        //
2tan⁡(3kx+x2)(12k+2)(tan⁡2(3kx+x2)+1)+2tan⁡(x(1−6k)2)(2−12k)(tan⁡2(x(1−6k)2)+1)\frac{2 \tan{\left(3 k x + \frac{x}{2} \right)}}{\left(12 k + 2\right) \left(\tan^{2}{\left(3 k x + \frac{x}{2} \right)} + 1\right)} + \frac{2 \tan{\left(\frac{x \left(1 - 6 k\right)}{2} \right)}}{\left(2 - 12 k\right) \left(\tan^{2}{\left(\frac{x \left(1 - 6 k\right)}{2} \right)} + 1\right)} 
                1                                    1                 
---------------------------------- + ----------------------------------
              /  pi              \                 /  pi              \
(2 - 12*k)*sec|- -- + x*(1 - 6*k)|   (2 + 12*k)*sec|- -- + x*(1 + 6*k)|
              \  2               /                 \  2               /
1(12k+2)sec⁡(x(6k+1)−π2)+1(2−12k)sec⁡(x(1−6k)−π2)\frac{1}{\left(12 k + 2\right) \sec{\left(x \left(6 k + 1\right) - \frac{\pi}{2} \right)}} + \frac{1}{\left(2 - 12 k\right) \sec{\left(x \left(1 - 6 k\right) - \frac{\pi}{2} \right)}} 
                                   /x        \        
                              2*tan|- + 3*k*x|        
  sin(x*(-1 + 6*k))                \2        /        
- ----------------- + --------------------------------
       2 - 12*k       /       2/x        \\           
                      |1 + tan |- + 3*k*x||*(2 + 12*k)
                      \        \2        //
2tan⁡(3kx+x2)(12k+2)(tan⁡2(3kx+x2)+1)−sin⁡(x(6k−1))2−12k\frac{2 \tan{\left(3 k x + \frac{x}{2} \right)}}{\left(12 k + 2\right) \left(\tan^{2}{\left(3 k x + \frac{x}{2} \right)} + 1\right)} - \frac{\sin{\left(x \left(6 k - 1\right) \right)}}{2 - 12 k} 
               /x*(-1 + 6*k)\                        /x        \        
          2*cot|------------|                   2*cot|- + 3*k*x|        
               \     2      /                        \2        /        
- ----------------------------------- + --------------------------------
  /       2/x*(-1 + 6*k)\\              /       2/x        \\           
  |1 + cot |------------||*(2 - 12*k)   |1 + cot |- + 3*k*x||*(2 + 12*k)
  \        \     2      //              \        \2        //
2cot⁡(3kx+x2)(12k+2)(cot⁡2(3kx+x2)+1)−2cot⁡(x(6k−1)2)(2−12k)(cot⁡2(x(6k−1)2)+1)\frac{2 \cot{\left(3 k x + \frac{x}{2} \right)}}{\left(12 k + 2\right) \left(\cot^{2}{\left(3 k x + \frac{x}{2} \right)} + 1\right)} - \frac{2 \cot{\left(\frac{x \left(6 k - 1\right)}{2} \right)}}{\left(2 - 12 k\right) \left(\cot^{2}{\left(\frac{x \left(6 k - 1\right)}{2} \right)} + 1\right)} 
     1                         sin(x + 6*k*x)
-----------*sin((1 - 6*k)*x) + --------------
2*(1 - 6*k)                     2*(1 + 6*k)
12(1−6k)sin⁡(x(1−6k))+sin⁡(6kx+x)2(6k+1)\frac{1}{2 \left(1 - 6 k\right)} \sin{\left(x \left(1 - 6 k\right) \right)} + \frac{\sin{\left(6 k x + x \right)}}{2 \left(6 k + 1\right)} 
               /x*(-1 + 6*k)\                        /x        \        
          2*tan|------------|                   2*tan|- + 3*k*x|        
               \     2      /                        \2        /        
- ----------------------------------- + --------------------------------
  /       2/x*(-1 + 6*k)\\              /       2/x        \\           
  |1 + tan |------------||*(2 - 12*k)   |1 + tan |- + 3*k*x||*(2 + 12*k)
  \        \     2      //              \        \2        //
2tan⁡(3kx+x2)(12k+2)(tan⁡2(3kx+x2)+1)−2tan⁡(x(6k−1)2)(2−12k)(tan⁡2(x(6k−1)2)+1)\frac{2 \tan{\left(3 k x + \frac{x}{2} \right)}}{\left(12 k + 2\right) \left(\tan^{2}{\left(3 k x + \frac{x}{2} \right)} + 1\right)} - \frac{2 \tan{\left(\frac{x \left(6 k - 1\right)}{2} \right)}}{\left(2 - 12 k\right) \left(\tan^{2}{\left(\frac{x \left(6 k - 1\right)}{2} \right)} + 1\right)} 
             /x*(1 - 6*k)\                        /x*(1 + 6*k)\        
        2*tan|-----------|                   2*tan|-----------|        
             \     2     /                        \     2     /        
---------------------------------- + ----------------------------------
/       2/x*(1 - 6*k)\\              /       2/x*(1 + 6*k)\\           
|1 + tan |-----------||*(2 - 12*k)   |1 + tan |-----------||*(2 + 12*k)
\        \     2     //              \        \     2     //
2tan⁡(x(6k+1)2)(12k+2)(tan⁡2(x(6k+1)2)+1)+2tan⁡(x(1−6k)2)(2−12k)(tan⁡2(x(1−6k)2)+1)\frac{2 \tan{\left(\frac{x \left(6 k + 1\right)}{2} \right)}}{\left(12 k + 2\right) \left(\tan^{2}{\left(\frac{x \left(6 k + 1\right)}{2} \right)} + 1\right)} + \frac{2 \tan{\left(\frac{x \left(1 - 6 k\right)}{2} \right)}}{\left(2 - 12 k\right) \left(\tan^{2}{\left(\frac{x \left(1 - 6 k\right)}{2} \right)} + 1\right)} 
2*tan(x*(1 - 6*k)/2)/((1 + tan(x*(1 - 6*k)/2)^2)*(2 - 12*k)) + 2*tan(x*(1 + 6*k)/2)/((1 + tan(x*(1 + 6*k)/2)^2)*(2 + 12*k))
Potencias [src] 
sin(x*(1 - 6*k))   sin(x*(1 + 6*k))
---------------- + ----------------
    2 - 12*k           2 + 12*k
sin⁡(x(6k+1))12k+2+sin⁡(x(1−6k))2−12k\frac{\sin{\left(x \left(6 k + 1\right) \right)}}{12 k + 2} + \frac{\sin{\left(x \left(1 - 6 k\right) \right)}}{2 - 12 k} 
    /   -I*x*(1 - 6*k)    I*x*(1 - 6*k)\     /   -I*x*(1 + 6*k)    I*x*(1 + 6*k)\
  I*\- e               + e             /   I*\- e               + e             /
- -------------------------------------- - --------------------------------------
               2*(2 - 12*k)                             2*(2 + 12*k)
−i(eix(6k+1)−e−ix(6k+1))2(12k+2)−i(eix(1−6k)−e−ix(1−6k))2(2−12k)- \frac{i \left(e^{i x \left(6 k + 1\right)} - e^{- i x \left(6 k + 1\right)}\right)}{2 \left(12 k + 2\right)} - \frac{i \left(e^{i x \left(1 - 6 k\right)} - e^{- i x \left(1 - 6 k\right)}\right)}{2 \left(2 - 12 k\right)} 
-i*(-exp(-i*x*(1 - 6*k)) + exp(i*x*(1 - 6*k)))/(2*(2 - 12*k)) - i*(-exp(-i*x*(1 + 6*k)) + exp(i*x*(1 + 6*k)))/(2*(2 + 12*k))
Combinatoria [src] 
-sin(x + 6*k*x) + 6*k*sin(x + 6*k*x) + 6*k*sin(-x + 6*k*x) + sin(-x + 6*k*x)
----------------------------------------------------------------------------
                           2*(1 + 6*k)*(-1 + 6*k)
6ksin⁡(6kx−x)+6ksin⁡(6kx+x)+sin⁡(6kx−x)−sin⁡(6kx+x)2(6k−1)(6k+1)\frac{6 k \sin{\left(6 k x - x \right)} + 6 k \sin{\left(6 k x + x \right)} + \sin{\left(6 k x - x \right)} - \sin{\left(6 k x + x \right)}}{2 \left(6 k - 1\right) \left(6 k + 1\right)} 
(-sin(x + 6*k*x) + 6*k*sin(x + 6*k*x) + 6*k*sin(-x + 6*k*x) + sin(-x + 6*k*x))/(2*(1 + 6*k)*(-1 + 6*k))
    © Sr Examen – Калькулятор