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¿cómo vas a descomponer esta expresión en fracciones?:
(y/(x*y-x^2)+x/(x*y-y^2))/(x^2+2*x*y+y^2)/(1/x+1/y)
(y/(x*y-x^2)+x/(x*y-y^2))/(((x^2+2*x*y+y^2)/(1/x+1/y)))
y/(y+2)+(1/(4-y^2)-1/(4-4*y+y^2))/2/(y-2)^2
y*(y+((1/(x+(x^2+y^2)^(1/2))*(1+(2*x/(2*(x^2+y^2)^(1/2)))))))
Factorizar el polinomio:
y^3-1/8
y^2+x*y-x^3+2*x^2-x*y^2+2*y^2
-y+a*y
y*x^2+x*z^2+z*y^2-y*z^2-x*y^2-z*x^2
Descomponer al cuadrado:
y^4+8*y^2-1
-y^4+7*y^2-4
y^4-8*y^2+1
y^4+8*y^2+1
Expresiones idénticas
tan(dos *x)^ cuatro *(diez + diez *tan(dos *x)^ dos)+ quince *cos(cinco *x)/(uno + tres *sin(cinco *x))
tangente de (2 multiplicar por x) en el grado 4 multiplicar por (10 más 10 multiplicar por tangente de (2 multiplicar por x) al cuadrado ) más 15 multiplicar por coseno de (5 multiplicar por x) dividir por (1 más 3 multiplicar por seno de (5 multiplicar por x))
tangente de (dos multiplicar por x) en el grado cuatro multiplicar por (diez más diez multiplicar por tangente de (dos multiplicar por x) en el grado dos) más quince multiplicar por coseno de (cinco multiplicar por x) dividir por (uno más tres multiplicar por seno de (cinco multiplicar por x))
tan(2*x)4*(10+10*tan(2*x)2)+15*cos(5*x)/(1+3*sin(5*x))
tan2*x4*10+10*tan2*x2+15*cos5*x/1+3*sin5*x
tan(2*x)⁴*(10+10*tan(2*x)²)+15*cos(5*x)/(1+3*sin(5*x))
tan(2*x) en el grado 4*(10+10*tan(2*x) en el grado 2)+15*cos(5*x)/(1+3*sin(5*x))
tan(2x)^4(10+10tan(2x)^2)+15cos(5x)/(1+3sin(5x))
tan(2x)4(10+10tan(2x)2)+15cos(5x)/(1+3sin(5x))
tan2x410+10tan2x2+15cos5x/1+3sin5x
tan2x^410+10tan2x^2+15cos5x/1+3sin5x
tan(2*x)^4*(10+10*tan(2*x)^2)+15*cos(5*x) dividir por (1+3*sin(5*x))
Expresiones semejantes
tan(2*x)^4*(10+10*tan(2*x)^2)+15*cos(5*x)/(1-3*sin(5*x))
tan(2*x)^4*(10+10*tan(2*x)^2)-15*cos(5*x)/(1+3*sin(5*x))
tan(2*x)^4*(10-10*tan(2*x)^2)+15*cos(5*x)/(1+3*sin(5*x))
Expresiones con funciones
Tangente tan
tan(2*x)/(tan(4*x)-tan(2*x))
tan(2*a)/(tan(4*a)-tan(2)*a)
tan(16*pi/5)*tan(pi+a)-cos(pi/(2+a))*sin(pi+a)
tan(3*n/2)*tan(n+a)-cos(n/(2+a))*sin(n+a)
tan(2*x)^2/(sqrt(1-x^2)*asin(x)^2)-(4+4*tan(2*x)^2)*tan(2*x)/asin(x)
Tangente tan
tan(2*x)/(tan(4*x)-tan(2*x))
tan(2*a)/(tan(4*a)-tan(2)*a)
tan(16*pi/5)*tan(pi+a)-cos(pi/(2+a))*sin(pi+a)
tan(3*n/2)*tan(n+a)-cos(n/(2+a))*sin(n+a)
tan(2*x)^2/(sqrt(1-x^2)*asin(x)^2)-(4+4*tan(2*x)^2)*tan(2*x)/asin(x)
Coseno cos
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)))
cos(x)/acos(x)+sin(x)/(sqrt(1-x^2)*acos(x)^2)
cos(x)^acot(x)*(-log(cos(x))/(1+x^2)-acot(x)*sin(x)/cos(x))
cos(x)/(1-cos(x))-sin(x)^2/(1-cos(x))^2
cos(x)/(1-sin(2*x))+2*cos(2*x)*sin(x)/(1-sin(2*x))^2
Seno sin
sin(x)/(9*cos(x))
sin(x)/(a*sqrt(1-cos(x)^((2/a)^2)))
sin((x+6)/3)^3/6-1/(((x+4)*log(2))*(x+4))-cos((x+6)/3)^2*sin((x+6)/3)/3
sin(x)^(sqrt(x))*(-3/(2*sqrt(x))+(log(sin(x))/sqrt(x)+2*sqrt(x)*cos(x)/sin(x))^3/8-3*(log(sin(x))/sqrt(x)+2*sqrt(x)*cos(x)/sin(x))*(4*sqrt(x)+log(sin(x))/x^(3/2)-4*cos(x)/(sqrt(x)*sin(x))+4*sqrt(x)*cos(x)^2/sin(x)^2)/8+3*log(sin(x))/(8*x^(5/2))+2*sqrt(x)*cos(x)^3/sin(x)^3+2*sqrt(x)*cos(x)/sin(x)-3*cos(x)^2/(2*sqrt(x)*sin(x)^2)-3*cos(x)/(4*x^(3/2)*sin(x)))
sin(x)/(3+cos(x))+(3-cos(x))*sin(x)/(3+cos(x))^2

Simplificación de expresiones/ Descomposición en fracciones simples/ tan(2*x)^4*(10+10*tan(2*x)^2)+15*cos(5*x)/(1+3*sin(5*x))

¿Cómo vas a descomponer esta tan(2x)^4(10+10tan(2x)^2)+15cos(5x)/(1+3sin(5x)) expresión en fracciones?

Solución

Ha introducido [src]

   4      /           2     \    15*cos(5*x)  
tan (2*x)*\10 + 10*tan (2*x)/ + --------------
                                1 + 3*sin(5*x)

\left(10 \tan^{2}{\left(2 x \right)} + 10\right) \tan^{4}{\left(2 x \right)} + \frac{15 \cos{\left(5 x \right)}}{3 \sin{\left(5 x \right)} + 1}

tan(2*x)^4*(10 + 10*tan(2*x)^2) + (15*cos(5*x))/(1 + 3*sin(5*x))

Simplificación general [src]

  /                  4                      \
  |             2*tan (2*x)*(1 + 3*sin(5*x))|
5*|3*cos(5*x) + ----------------------------|
  |                         2               |
  \                      cos (2*x)          /
---------------------------------------------
                1 + 3*sin(5*x)

\frac{5 \left(\frac{2 \left(3 \sin{\left(5 x \right)} + 1\right) \tan^{4}{\left(2 x \right)}}{\cos^{2}{\left(2 x \right)}} + 3 \cos{\left(5 x \right)}\right)}{3 \sin{\left(5 x \right)} + 1}

5*(3*cos(5*x) + 2*tan(2*x)^4*(1 + 3*sin(5*x))/cos(2*x)^2)/(1 + 3*sin(5*x))

Respuesta numérica [src]

tan(2*x)^4*(10.0 + 10.0*tan(2*x)^2) + 15.0*cos(5*x)/(1.0 + 3.0*sin(5*x))

tan(2*x)^4*(10.0 + 10.0*tan(2*x)^2) + 15.0*cos(5*x)/(1.0 + 3.0*sin(5*x))

Denominador común [src]

      4              6         15*cos(5*x)  
10*tan (2*x) + 10*tan (2*x) + --------------
                              1 + 3*sin(5*x)

10 \tan^{6}{\left(2 x \right)} + 10 \tan^{4}{\left(2 x \right)} + \frac{15 \cos{\left(5 x \right)}}{3 \sin{\left(5 x \right)} + 1}

10*tan(2*x)^4 + 10*tan(2*x)^6 + 15*cos(5*x)/(1 + 3*sin(5*x))

Denominador racional [src]

                 4                       /           2     \
15*cos(5*x) + tan (2*x)*(1 + 3*sin(5*x))*\10 + 10*tan (2*x)/
------------------------------------------------------------
                       1 + 3*sin(5*x)

\frac{\left(3 \sin{\left(5 x \right)} + 1\right) \left(10 \tan^{2}{\left(2 x \right)} + 10\right) \tan^{4}{\left(2 x \right)} + 15 \cos{\left(5 x \right)}}{3 \sin{\left(5 x \right)} + 1}

(15*cos(5*x) + tan(2*x)^4*(1 + 3*sin(5*x))*(10 + 10*tan(2*x)^2))/(1 + 3*sin(5*x))

Combinatoria [src]

  /     4             6                          4                      6              \
5*\2*tan (2*x) + 2*tan (2*x) + 3*cos(5*x) + 6*tan (2*x)*sin(5*x) + 6*tan (2*x)*sin(5*x)/
----------------------------------------------------------------------------------------
                                     1 + 3*sin(5*x)

\frac{5 \left(6 \sin{\left(5 x \right)} \tan^{6}{\left(2 x \right)} + 6 \sin{\left(5 x \right)} \tan^{4}{\left(2 x \right)} + 3 \cos{\left(5 x \right)} + 2 \tan^{6}{\left(2 x \right)} + 2 \tan^{4}{\left(2 x \right)}\right)}{3 \sin{\left(5 x \right)} + 1}

5*(2*tan(2*x)^4 + 2*tan(2*x)^6 + 3*cos(5*x) + 6*tan(2*x)^4*sin(5*x) + 6*tan(2*x)^6*sin(5*x))/(1 + 3*sin(5*x))

Potencias [src]

                                                     /                            2\
                                                   4 |        /   2*I*x    -2*I*x\ |
                               /   2*I*x    -2*I*x\  |     10*\- e      + e      / |
       -5*I*x       5*I*x      \- e      + e      / *|10 - ------------------------|
   15*e         15*e                                 |                         2   |
   ---------- + ---------                            |       / -2*I*x    2*I*x\    |
       2            2                                \       \e       + e     /    /
---------------------------- + -----------------------------------------------------
        /   -5*I*x    5*I*x\                                      4                 
    3*I*\- e       + e     /                    / -2*I*x    2*I*x\                  
1 - ------------------------                    \e       + e     /                  
               2

\frac{\left(- \frac{10 \left(- e^{2 i x} + e^{- 2 i x}\right)^{2}}{\left(e^{2 i x} + e^{- 2 i x}\right)^{2}} + 10\right) \left(- e^{2 i x} + e^{- 2 i x}\right)^{4}}{\left(e^{2 i x} + e^{- 2 i x}\right)^{4}} + \frac{\frac{15 e^{5 i x}}{2} + \frac{15 e^{- 5 i x}}{2}}{- \frac{3 i \left(e^{5 i x} - e^{- 5 i x}\right)}{2} + 1}

(15*exp(-5*i*x)/2 + 15*exp(5*i*x)/2)/(1 - 3*i*(-exp(-5*i*x) + exp(5*i*x))/2) + (-exp(2*i*x) + exp(-2*i*x))^4*(10 - 10*(-exp(2*i*x) + exp(-2*i*x))^2/(exp(-2*i*x) + exp(2*i*x))^2)/(exp(-2*i*x) + exp(2*i*x))^4

Unión de expresiones racionales [src]

  /                  4      /       2     \                 \
5*\3*cos(5*x) + 2*tan (2*x)*\1 + tan (2*x)/*(1 + 3*sin(5*x))/
-------------------------------------------------------------
                        1 + 3*sin(5*x)

\frac{5 \left(2 \left(3 \sin{\left(5 x \right)} + 1\right) \left(\tan^{2}{\left(2 x \right)} + 1\right) \tan^{4}{\left(2 x \right)} + 3 \cos{\left(5 x \right)}\right)}{3 \sin{\left(5 x \right)} + 1}

5*(3*cos(5*x) + 2*tan(2*x)^4*(1 + tan(2*x)^2)*(1 + 3*sin(5*x)))/(1 + 3*sin(5*x))

Abrimos la expresión [src]

                       3                                                                                       4                                             5                                                           6                                    
                300*cos (x)                                75*cos(x)                                    160*tan (x)                                   240*cos (x)                                                 640*tan (x)                                 
- --------------------------------------- + --------------------------------------- + ----------------------------------------------- + --------------------------------------- + ----------------------------------------------------------------------------
            3                        5                3                        5             8           2           6           4                3                        5             12            6           2           10            4            8   
  1 - 60*sin (x) + 15*sin(x) + 48*sin (x)   1 - 60*sin (x) + 15*sin(x) + 48*sin (x)   1 + tan (x) - 4*tan (x) - 4*tan (x) + 6*tan (x)   1 - 60*sin (x) + 15*sin(x) + 48*sin (x)   1 + tan  (x) - 20*tan (x) - 6*tan (x) - 6*tan  (x) + 15*tan (x) + 15*tan (x)

\frac{640 \tan^{6}{\left(x \right)}}{\tan^{12}{\left(x \right)} - 6 \tan^{10}{\left(x \right)} + 15 \tan^{8}{\left(x \right)} - 20 \tan^{6}{\left(x \right)} + 15 \tan^{4}{\left(x \right)} - 6 \tan^{2}{\left(x \right)} + 1} + \frac{160 \tan^{4}{\left(x \right)}}{\tan^{8}{\left(x \right)} - 4 \tan^{6}{\left(x \right)} + 6 \tan^{4}{\left(x \right)} - 4 \tan^{2}{\left(x \right)} + 1} + \frac{240 \cos^{5}{\left(x \right)}}{48 \sin^{5}{\left(x \right)} - 60 \sin^{3}{\left(x \right)} + 15 \sin{\left(x \right)} + 1} - \frac{300 \cos^{3}{\left(x \right)}}{48 \sin^{5}{\left(x \right)} - 60 \sin^{3}{\left(x \right)} + 15 \sin{\left(x \right)} + 1} + \frac{75 \cos{\left(x \right)}}{48 \sin^{5}{\left(x \right)} - 60 \sin^{3}{\left(x \right)} + 15 \sin{\left(x \right)} + 1}

-300*cos(x)^3/(1 - 60*sin(x)^3 + 15*sin(x) + 48*sin(x)^5) + 75*cos(x)/(1 - 60*sin(x)^3 + 15*sin(x) + 48*sin(x)^5) + 160*tan(x)^4/(1 + tan(x)^8 - 4*tan(x)^2 - 4*tan(x)^6 + 6*tan(x)^4) + 240*cos(x)^5/(1 - 60*sin(x)^3 + 15*sin(x) + 48*sin(x)^5) + 640*tan(x)^6/(1 + tan(x)^12 - 20*tan(x)^6 - 6*tan(x)^2 - 6*tan(x)^10 + 15*tan(x)^4 + 15*tan(x)^8)

Parte trigonométrica [src]

         10            15*cos(5*x)  
------------------- + --------------
   6         4        1 + 3*sin(5*x)
cos (2*x)*csc (2*x)

\frac{10}{\cos^{6}{\left(2 x \right)} \csc^{4}{\left(2 x \right)}} + \frac{15 \cos{\left(5 x \right)}}{3 \sin{\left(5 x \right)} + 1}

   /           2/5*x\   \                            
   |      8*cot |---|   |                            
   |            \ 4 /   |                            
15*|1 - ----------------|                            
   |                   2|                            
   |    /       2/5*x\\ |                       2    
   |    |1 + cot |---|| |          /       2   \     
   \    \        \ 4 // /       10*\1 + cot (x)/     
------------------------- + -------------------------
               /5*x\                      2          
          6*cot|---|        /        2   \     4     
               \ 2 /        \-1 + cot (x)/ *cot (2*x)
    1 + -------------                                
               2/5*x\                                
        1 + cot |---|                                
                \ 2 /

\frac{15 \left(1 - \frac{8 \cot^{2}{\left(\frac{5 x}{4} \right)}}{\left(\cot^{2}{\left(\frac{5 x}{4} \right)} + 1\right)^{2}}\right)}{1 + \frac{6 \cot{\left(\frac{5 x}{2} \right)}}{\cot^{2}{\left(\frac{5 x}{2} \right)} + 1}} + \frac{10 \left(\cot^{2}{\left(x \right)} + 1\right)^{2}}{\left(\cot^{2}{\left(x \right)} - 1\right)^{2} \cot^{4}{\left(2 x \right)}}

      6/pi      \                               
10*csc |-- - 2*x|                               
       \2       /                15             
----------------- + ----------------------------
       4            /       3    \    /pi      \
    csc (2*x)       |1 + --------|*csc|-- - 5*x|
                    \    csc(5*x)/    \2       /

\frac{10 \csc^{6}{\left(- 2 x + \frac{\pi}{2} \right)}}{\csc^{4}{\left(2 x \right)}} + \frac{15}{\left(1 + \frac{3}{\csc{\left(5 x \right)}}\right) \csc{\left(- 5 x + \frac{\pi}{2} \right)}}

                  /         2/5*x\\
      4        15*|1 - 2*sin |---||
10*tan (2*x)      \          \ 2 //
------------ + --------------------
    2             1 + 3*sin(5*x)   
 cos (2*x)

\frac{15 \left(1 - 2 \sin^{2}{\left(\frac{5 x}{2} \right)}\right)}{3 \sin{\left(5 x \right)} + 1} + \frac{10 \tan^{4}{\left(2 x \right)}}{\cos^{2}{\left(2 x \right)}}

                                            /       2/5*x\\        
                                         15*|1 - tan |---||        
   4      /           2     \               \        \ 2 //        
tan (2*x)*\10 + 10*tan (2*x)/ + -----------------------------------
                                                /           /5*x\ \
                                                |      6*tan|---| |
                                /       2/5*x\\ |           \ 2 / |
                                |1 + tan |---||*|1 + -------------|
                                \        \ 2 // |           2/5*x\|
                                                |    1 + tan |---||
                                                \            \ 2 //

\left(10 \tan^{2}{\left(2 x \right)} + 10\right) \tan^{4}{\left(2 x \right)} + \frac{15 \left(1 - \tan^{2}{\left(\frac{5 x}{2} \right)}\right)}{\left(1 + \frac{6 \tan{\left(\frac{5 x}{2} \right)}}{\tan^{2}{\left(\frac{5 x}{2} \right)} + 1}\right) \left(\tan^{2}{\left(\frac{5 x}{2} \right)} + 1\right)}

                           /           2     \
                    4      |     10*sin (2*x)|
                 sin (2*x)*|10 + ------------|
                           |         2       |
 15*cos(5*x)               \      cos (2*x)  /
-------------- + -----------------------------
1 + 3*sin(5*x)                4               
                           cos (2*x)

\frac{\left(\frac{10 \sin^{2}{\left(2 x \right)}}{\cos^{2}{\left(2 x \right)}} + 10\right) \sin^{4}{\left(2 x \right)}}{\cos^{4}{\left(2 x \right)}} + \frac{15 \cos{\left(5 x \right)}}{3 \sin{\left(5 x \right)} + 1}

                       4         4     
 15*cos(5*x)     10*sec (2*x)*sin (2*x)
-------------- + ----------------------
1 + 3*sin(5*x)            2            
                       cos (2*x)

\frac{10 \sin^{4}{\left(2 x \right)} \sec^{4}{\left(2 x \right)}}{\cos^{2}{\left(2 x \right)}} + \frac{15 \cos{\left(5 x \right)}}{3 \sin{\left(5 x \right)} + 1}

                           8        
 15*cos(5*x)        160*sin (2*x)   
-------------- + -------------------
1 + 3*sin(5*x)      2         4     
                 cos (2*x)*sin (4*x)

\frac{160 \sin^{8}{\left(2 x \right)}}{\sin^{4}{\left(4 x \right)} \cos^{2}{\left(2 x \right)}} + \frac{15 \cos{\left(5 x \right)}}{3 \sin{\left(5 x \right)} + 1}

                            4          
 15*cos(5*x)          10*tan (2*x)     
-------------- + ----------------------
1 + 3*sin(5*x)                2        
                 /       2   \     4   
                 \1 - tan (x)/ *cos (x)

\frac{15 \cos{\left(5 x \right)}}{3 \sin{\left(5 x \right)} + 1} + \frac{10 \tan^{4}{\left(2 x \right)}}{\left(1 - \tan^{2}{\left(x \right)}\right)^{2} \cos^{4}{\left(x \right)}}

   /         2/5*x\\                      
15*|1 - 2*sin |---||          4       4   
   \          \ 2 //   160*cos (x)*sin (x)
-------------------- + -------------------
   1 + 3*sin(5*x)                       6 
                        /          2   \  
                        \-1 + 2*sin (x)/

\frac{15 \left(1 - 2 \sin^{2}{\left(\frac{5 x}{2} \right)}\right)}{3 \sin{\left(5 x \right)} + 1} + \frac{160 \sin^{4}{\left(x \right)} \cos^{4}{\left(x \right)}}{\left(2 \sin^{2}{\left(x \right)} - 1\right)^{6}}

           /        2/5*x\\                            2        
        15*|-1 + cot |---||               /       2   \     4   
           \         \ 2 //           160*\1 + cot (x)/ *cot (x)
----------------------------------- + --------------------------
                /           /5*x\ \                      6      
                |      6*cot|---| |        /        2   \       
/       2/5*x\\ |           \ 2 / |        \-1 + cot (x)/       
|1 + cot |---||*|1 + -------------|                             
\        \ 2 // |           2/5*x\|                             
                |    1 + cot |---||                             
                \            \ 2 //

\frac{160 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \cot^{4}{\left(x \right)}}{\left(\cot^{2}{\left(x \right)} - 1\right)^{6}} + \frac{15 \left(\cot^{2}{\left(\frac{5 x}{2} \right)} - 1\right)}{\left(1 + \frac{6 \cot{\left(\frac{5 x}{2} \right)}}{\cot^{2}{\left(\frac{5 x}{2} \right)} + 1}\right) \left(\cot^{2}{\left(\frac{5 x}{2} \right)} + 1\right)}

                           4        
 15*cos(5*x)         10*sec (2*x)   
-------------- + -------------------
1 + 3*sin(5*x)      2         4     
                 cos (2*x)*csc (2*x)

\frac{10 \sec^{4}{\left(2 x \right)}}{\cos^{2}{\left(2 x \right)} \csc^{4}{\left(2 x \right)}} + \frac{15 \cos{\left(5 x \right)}}{3 \sin{\left(5 x \right)} + 1}

                                   8/      pi\     
                            320*cos |2*x - --|     
    15*cos(5*x)                     \      2 /     
------------------- + -----------------------------
         /      pi\                     4/      pi\
1 + 3*cos|5*x - --|   (1 + cos(4*x))*cos |4*x - --|
         \      2 /                      \      2 /

\frac{15 \cos{\left(5 x \right)}}{3 \cos{\left(5 x - \frac{\pi}{2} \right)} + 1} + \frac{320 \cos^{8}{\left(2 x - \frac{\pi}{2} \right)}}{\left(\cos{\left(4 x \right)} + 1\right) \cos^{4}{\left(4 x - \frac{\pi}{2} \right)}}

      4                      
10*sin (2*x)    15*cos(5*x)  
------------ + --------------
    6          1 + 3*sin(5*x)
 cos (2*x)

\frac{10 \sin^{4}{\left(2 x \right)}}{\cos^{6}{\left(2 x \right)}} + \frac{15 \cos{\left(5 x \right)}}{3 \sin{\left(5 x \right)} + 1}

           /        2/5*x\\                                       4                
        15*|-1 + cot |---||                        /       2     \     8           
           \         \ 2 //                   5120*\1 + cot (2*x)/ *cot (x)        
----------------------------------- + ---------------------------------------------
                /           /5*x\ \                8 /            2     \          
                |      6*cot|---| |   /       2   \  |    -1 + cot (2*x)|    4     
/       2/5*x\\ |           \ 2 / |   \1 + cot (x)/ *|1 + --------------|*cot (2*x)
|1 + cot |---||*|1 + -------------|                  |           2      |          
\        \ 2 // |           2/5*x\|                  \    1 + cot (2*x) /          
                |    1 + cot |---||                                                
                \            \ 2 //

\frac{5120 \left(\cot^{2}{\left(2 x \right)} + 1\right)^{4} \cot^{8}{\left(x \right)}}{\left(\frac{\cot^{2}{\left(2 x \right)} - 1}{\cot^{2}{\left(2 x \right)} + 1} + 1\right) \left(\cot^{2}{\left(x \right)} + 1\right)^{8} \cot^{4}{\left(2 x \right)}} + \frac{15 \left(\cot^{2}{\left(\frac{5 x}{2} \right)} - 1\right)}{\left(1 + \frac{6 \cot{\left(\frac{5 x}{2} \right)}}{\cot^{2}{\left(\frac{5 x}{2} \right)} + 1}\right) \left(\cot^{2}{\left(\frac{5 x}{2} \right)} + 1\right)}

      6         4         15*cos(5*x)  
10*sec (2*x)*sin (2*x) + --------------
                         1 + 3*sin(5*x)

10 \sin^{4}{\left(2 x \right)} \sec^{6}{\left(2 x \right)} + \frac{15 \cos{\left(5 x \right)}}{3 \sin{\left(5 x \right)} + 1}

                                /           4     \
                         8      |     40*sin (2*x)|
      /pi      \   16*sin (2*x)*|10 + ------------|
15*sin|-- + 5*x|                |         2       |
      \2       /                \      sin (4*x)  /
---------------- + --------------------------------
 1 + 3*sin(5*x)                  4                 
                              sin (4*x)

\frac{16 \left(\frac{40 \sin^{4}{\left(2 x \right)}}{\sin^{2}{\left(4 x \right)}} + 10\right) \sin^{8}{\left(2 x \right)}}{\sin^{4}{\left(4 x \right)}} + \frac{15 \sin{\left(5 x + \frac{\pi}{2} \right)}}{3 \sin{\left(5 x \right)} + 1}

            /       2/5*x\\                            2        
         15*|1 - tan |---||               /       2   \     4   
            \        \ 2 //           160*\1 + tan (x)/ *tan (x)
----------------------------------- + --------------------------
                /           /5*x\ \                      6      
                |      6*tan|---| |         /       2   \       
/       2/5*x\\ |           \ 2 / |         \1 - tan (x)/       
|1 + tan |---||*|1 + -------------|                             
\        \ 2 // |           2/5*x\|                             
                |    1 + tan |---||                             
                \            \ 2 //

\frac{160 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \tan^{4}{\left(x \right)}}{\left(1 - \tan^{2}{\left(x \right)}\right)^{6}} + \frac{15 \left(1 - \tan^{2}{\left(\frac{5 x}{2} \right)}\right)}{\left(1 + \frac{6 \tan{\left(\frac{5 x}{2} \right)}}{\tan^{2}{\left(\frac{5 x}{2} \right)} + 1}\right) \left(\tan^{2}{\left(\frac{5 x}{2} \right)} + 1\right)}

   /         2/5*x\\                         
15*|1 - 2*sin |---||               4         
   \          \ 2 //        160*tan (x)      
-------------------- + ----------------------
   1 + 3*sin(5*x)                   6        
                       /       2   \     4   
                       \1 - tan (x)/ *cos (x)

\frac{15 \left(1 - 2 \sin^{2}{\left(\frac{5 x}{2} \right)}\right)}{3 \sin{\left(5 x \right)} + 1} + \frac{160 \tan^{4}{\left(x \right)}}{\left(1 - \tan^{2}{\left(x \right)}\right)^{6} \cos^{4}{\left(x \right)}}

                                    /           2     \
                             4      |     10*sec (2*x)|
                          sec (2*x)*|10 + ------------|
                                    |         2       |
           15                       \      csc (2*x)  /
----------------------- + -----------------------------
/       3    \                         4               
|1 + --------|*sec(5*x)             csc (2*x)          
\    csc(5*x)/

\frac{\left(10 + \frac{10 \sec^{2}{\left(2 x \right)}}{\csc^{2}{\left(2 x \right)}}\right) \sec^{4}{\left(2 x \right)}}{\csc^{4}{\left(2 x \right)}} + \frac{15}{\left(1 + \frac{3}{\csc{\left(5 x \right)}}\right) \sec{\left(5 x \right)}}

                                         /            2      \
                                  4      |      10*sec (2*x) |
                               sec (2*x)*|10 + --------------|
                                         |        2/      pi\|
                                         |     sec |2*x - --||
             15                          \         \      2 //
---------------------------- + -------------------------------
/          3      \                        4/      pi\        
|1 + -------------|*sec(5*x)            sec |2*x - --|        
|       /      pi\|                         \      2 /        
|    sec|5*x - --||                                           
\       \      2 //

\frac{\left(\frac{10 \sec^{2}{\left(2 x \right)}}{\sec^{2}{\left(2 x - \frac{\pi}{2} \right)}} + 10\right) \sec^{4}{\left(2 x \right)}}{\sec^{4}{\left(2 x - \frac{\pi}{2} \right)}} + \frac{15}{\left(1 + \frac{3}{\sec{\left(5 x - \frac{\pi}{2} \right)}}\right) \sec{\left(5 x \right)}}

                             4           
 15*cos(5*x)          320*csc (4*x)      
-------------- + ------------------------
1 + 3*sin(5*x)                     8     
                 (1 + cos(4*x))*csc (2*x)

\frac{320 \csc^{4}{\left(4 x \right)}}{\left(\cos{\left(4 x \right)} + 1\right) \csc^{8}{\left(2 x \right)}} + \frac{15 \cos{\left(5 x \right)}}{3 \sin{\left(5 x \right)} + 1}

                       /        2    \
                    15*|1 - ---------|
      6/pi      \      |       2/5*x\|
10*csc |-- - 2*x|      |    csc |---||
       \2       /      \        \ 2 //
----------------- + ------------------
       4                      3       
    csc (2*x)          1 + --------   
                           csc(5*x)

\frac{15 \left(1 - \frac{2}{\csc^{2}{\left(\frac{5 x}{2} \right)}}\right)}{1 + \frac{3}{\csc{\left(5 x \right)}}} + \frac{10 \csc^{6}{\left(- 2 x + \frac{\pi}{2} \right)}}{\csc^{4}{\left(2 x \right)}}

      4                      
10*tan (2*x)    15*cos(5*x)  
------------ + --------------
    2          1 + 3*sin(5*x)
 cos (2*x)

\frac{10 \tan^{4}{\left(2 x \right)}}{\cos^{2}{\left(2 x \right)}} + \frac{15 \cos{\left(5 x \right)}}{3 \sin{\left(5 x \right)} + 1}

                                              4             
             15                        320*csc (4*x)        
---------------------------- + -----------------------------
/       3    \    /pi      \   /          1      \    8     
|1 + --------|*csc|-- - 5*x|   |1 + -------------|*csc (2*x)
\    csc(5*x)/    \2       /   |       /pi      \|          
                               |    csc|-- - 4*x||          
                               \       \2       //

\frac{320 \csc^{4}{\left(4 x \right)}}{\left(1 + \frac{1}{\csc{\left(- 4 x + \frac{\pi}{2} \right)}}\right) \csc^{8}{\left(2 x \right)}} + \frac{15}{\left(1 + \frac{3}{\csc{\left(5 x \right)}}\right) \csc{\left(- 5 x + \frac{\pi}{2} \right)}}

            /       2/5*x\\                                      4                
         15*|1 - tan |---||                       /       2     \     8           
            \        \ 2 //                  5120*\1 + tan (2*x)/ *tan (x)        
----------------------------------- + --------------------------------------------
                /           /5*x\ \                8 /           2     \          
                |      6*tan|---| |   /       2   \  |    1 - tan (2*x)|    4     
/       2/5*x\\ |           \ 2 / |   \1 + tan (x)/ *|1 + -------------|*tan (2*x)
|1 + tan |---||*|1 + -------------|                  |           2     |          
\        \ 2 // |           2/5*x\|                  \    1 + tan (2*x)/          
                |    1 + tan |---||                                               
                \            \ 2 //

\frac{5120 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{4} \tan^{8}{\left(x \right)}}{\left(\frac{1 - \tan^{2}{\left(2 x \right)}}{\tan^{2}{\left(2 x \right)} + 1} + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)^{8} \tan^{4}{\left(2 x \right)}} + \frac{15 \left(1 - \tan^{2}{\left(\frac{5 x}{2} \right)}\right)}{\left(1 + \frac{6 \tan{\left(\frac{5 x}{2} \right)}}{\tan^{2}{\left(\frac{5 x}{2} \right)} + 1}\right) \left(\tan^{2}{\left(\frac{5 x}{2} \right)} + 1\right)}

                                     /           2/      pi\\
                                     |     10*cos |2*x - --||
                         4/      pi\ |            \      2 /|
                      cos |2*x - --|*|10 + -----------------|
                          \      2 / |            2         |
    15*cos(5*x)                      \         cos (2*x)    /
------------------- + ---------------------------------------
         /      pi\                     4                    
1 + 3*cos|5*x - --|                  cos (2*x)               
         \      2 /

\frac{\left(10 + \frac{10 \cos^{2}{\left(2 x - \frac{\pi}{2} \right)}}{\cos^{2}{\left(2 x \right)}}\right) \cos^{4}{\left(2 x - \frac{\pi}{2} \right)}}{\cos^{4}{\left(2 x \right)}} + \frac{15 \cos{\left(5 x \right)}}{3 \cos{\left(5 x - \frac{\pi}{2} \right)} + 1}

                                            4/      pi\     
                                     320*sec |4*x - --|     
             15                              \      2 /     
---------------------------- + -----------------------------
/          3      \            /       1    \    8/      pi\
|1 + -------------|*sec(5*x)   |1 + --------|*sec |2*x - --|
|       /      pi\|            \    sec(4*x)/     \      2 /
|    sec|5*x - --||                                         
\       \      2 //

\frac{15}{\left(1 + \frac{3}{\sec{\left(5 x - \frac{\pi}{2} \right)}}\right) \sec{\left(5 x \right)}} + \frac{320 \sec^{4}{\left(4 x - \frac{\pi}{2} \right)}}{\left(1 + \frac{1}{\sec{\left(4 x \right)}}\right) \sec^{8}{\left(2 x - \frac{\pi}{2} \right)}}

                                              /           2/pi      \\
                                              |     10*csc |-- - 2*x||
                                  4/pi      \ |            \2       /|
                               csc |-- - 2*x|*|10 + -----------------|
                                   \2       / |            2         |
             15                               \         csc (2*x)    /
---------------------------- + ---------------------------------------
/       3    \    /pi      \                     4                    
|1 + --------|*csc|-- - 5*x|                  csc (2*x)               
\    csc(5*x)/    \2       /

\frac{\left(10 + \frac{10 \csc^{2}{\left(- 2 x + \frac{\pi}{2} \right)}}{\csc^{2}{\left(2 x \right)}}\right) \csc^{4}{\left(- 2 x + \frac{\pi}{2} \right)}}{\csc^{4}{\left(2 x \right)}} + \frac{15}{\left(1 + \frac{3}{\csc{\left(5 x \right)}}\right) \csc{\left(- 5 x + \frac{\pi}{2} \right)}}

   /           2/5*x\   \                              
   |      8*tan |---|   |                              
   |            \ 4 /   |                              
15*|1 - ----------------|                              
   |                   2|                              
   |    /       2/5*x\\ |                   2          
   |    |1 + tan |---|| |      /       2   \     4     
   \    \        \ 4 // /   10*\1 + tan (x)/ *tan (2*x)
------------------------- + ---------------------------
               /5*x\                            2      
          6*tan|---|               /       2   \       
               \ 2 /               \1 - tan (x)/       
    1 + -------------                                  
               2/5*x\                                  
        1 + tan |---|                                  
                \ 2 /

\frac{15 \left(1 - \frac{8 \tan^{2}{\left(\frac{5 x}{4} \right)}}{\left(\tan^{2}{\left(\frac{5 x}{4} \right)} + 1\right)^{2}}\right)}{1 + \frac{6 \tan{\left(\frac{5 x}{2} \right)}}{\tan^{2}{\left(\frac{5 x}{2} \right)} + 1}} + \frac{10 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \tan^{4}{\left(2 x \right)}}{\left(1 - \tan^{2}{\left(x \right)}\right)^{2}}

                             4          
 15*cos(5*x)           10*tan (2*x)     
-------------- + -----------------------
1 + 3*sin(5*x)                 2        
                 /        2   \     4   
                 \-1 + cot (x)/ *sin (x)

\frac{10 \tan^{4}{\left(2 x \right)}}{\left(\cot^{2}{\left(x \right)} - 1\right)^{2} \sin^{4}{\left(x \right)}} + \frac{15 \cos{\left(5 x \right)}}{3 \sin{\left(5 x \right)} + 1}

      4/      pi\      /         2/  pi   5*x\\
10*cos |2*x - --|   15*|1 - 2*cos |- -- + ---||
       \      2 /      \          \  2     2 //
----------------- + ---------------------------
       6                         /      pi\    
    cos (2*x)           1 + 3*cos|5*x - --|    
                                 \      2 /

\frac{15 \left(1 - 2 \cos^{2}{\left(\frac{5 x}{2} - \frac{\pi}{2} \right)}\right)}{3 \cos{\left(5 x - \frac{\pi}{2} \right)} + 1} + \frac{10 \cos^{4}{\left(2 x - \frac{\pi}{2} \right)}}{\cos^{6}{\left(2 x \right)}}

                       /pi      \
       4         15*sin|-- + 5*x|
 10*sin (2*x)          \2       /
-------------- + ----------------
   6/pi      \    1 + 3*sin(5*x) 
sin |-- + 2*x|                   
    \2       /

\frac{10 \sin^{4}{\left(2 x \right)}}{\sin^{6}{\left(2 x + \frac{\pi}{2} \right)}} + \frac{15 \sin{\left(5 x + \frac{\pi}{2} \right)}}{3 \sin{\left(5 x \right)} + 1}

   /         2/5*x\\                          
15*|1 - 2*sin |---||                4         
   \          \ 2 //         160*cot (x)      
-------------------- + -----------------------
   1 + 3*sin(5*x)                    6        
                       /        2   \     4   
                       \-1 + cot (x)/ *sin (x)

\frac{15 \left(1 - 2 \sin^{2}{\left(\frac{5 x}{2} \right)}\right)}{3 \sin{\left(5 x \right)} + 1} + \frac{160 \cot^{4}{\left(x \right)}}{\left(\cot^{2}{\left(x \right)} - 1\right)^{6} \sin^{4}{\left(x \right)}}

      4/      pi\                      
10*cos |2*x - --|                      
       \      2 /       15*cos(5*x)    
----------------- + -------------------
       6                     /      pi\
    cos (2*x)       1 + 3*cos|5*x - --|
                             \      2 /

\frac{10 \cos^{4}{\left(2 x - \frac{\pi}{2} \right)}}{\cos^{6}{\left(2 x \right)}} + \frac{15 \cos{\left(5 x \right)}}{3 \cos{\left(5 x - \frac{\pi}{2} \right)} + 1}

      /pi      \                                
15*sin|-- + 5*x|                  8             
      \2       /           320*sin (2*x)        
---------------- + -----------------------------
 1 + 3*sin(5*x)    /       /pi      \\    4     
                   |1 + sin|-- + 4*x||*sin (4*x)
                   \       \2       //

\frac{320 \sin^{8}{\left(2 x \right)}}{\left(\sin{\left(4 x + \frac{\pi}{2} \right)} + 1\right) \sin^{4}{\left(4 x \right)}} + \frac{15 \sin{\left(5 x + \frac{\pi}{2} \right)}}{3 \sin{\left(5 x \right)} + 1}

         10                                         
10 + ---------              /        2/5*x\\        
        2                15*|-1 + cot |---||        
     cot (2*x)              \         \ 2 //        
-------------- + -----------------------------------
     4                           /           /5*x\ \
  cot (2*x)                      |      6*cot|---| |
                 /       2/5*x\\ |           \ 2 / |
                 |1 + cot |---||*|1 + -------------|
                 \        \ 2 // |           2/5*x\|
                                 |    1 + cot |---||
                                 \            \ 2 //

\frac{10 + \frac{10}{\cot^{2}{\left(2 x \right)}}}{\cot^{4}{\left(2 x \right)}} + \frac{15 \left(\cot^{2}{\left(\frac{5 x}{2} \right)} - 1\right)}{\left(1 + \frac{6 \cot{\left(\frac{5 x}{2} \right)}}{\cot^{2}{\left(\frac{5 x}{2} \right)} + 1}\right) \left(\cot^{2}{\left(\frac{5 x}{2} \right)} + 1\right)}

                              /           4     \
                       8      |     40*sin (2*x)|
                 16*sin (2*x)*|10 + ------------|
                              |         2       |
 15*cos(5*x)                  \      sin (4*x)  /
-------------- + --------------------------------
1 + 3*sin(5*x)                 4                 
                            sin (4*x)

\frac{16 \left(\frac{40 \sin^{4}{\left(2 x \right)}}{\sin^{2}{\left(4 x \right)}} + 10\right) \sin^{8}{\left(2 x \right)}}{\sin^{4}{\left(4 x \right)}} + \frac{15 \cos{\left(5 x \right)}}{3 \sin{\left(5 x \right)} + 1}

       6                                     
 10*sec (2*x)                 15             
-------------- + ----------------------------
   4/      pi\   /          3      \         
sec |2*x - --|   |1 + -------------|*sec(5*x)
    \      2 /   |       /      pi\|         
                 |    sec|5*x - --||         
                 \       \      2 //

\frac{10 \sec^{6}{\left(2 x \right)}}{\sec^{4}{\left(2 x - \frac{\pi}{2} \right)}} + \frac{15}{\left(1 + \frac{3}{\sec{\left(5 x - \frac{\pi}{2} \right)}}\right) \sec{\left(5 x \right)}}

                    /           2        \
                 15*|1 - ----------------|
                    |       2/  pi   5*x\|
       6            |    sec |- -- + ---||
 10*sec (2*x)       \        \  2     2 //
-------------- + -------------------------
   4/      pi\                 3          
sec |2*x - --|       1 + -------------    
    \      2 /              /      pi\    
                         sec|5*x - --|    
                            \      2 /

\frac{15 \left(1 - \frac{2}{\sec^{2}{\left(\frac{5 x}{2} - \frac{\pi}{2} \right)}}\right)}{1 + \frac{3}{\sec{\left(5 x - \frac{\pi}{2} \right)}}} + \frac{10 \sec^{6}{\left(2 x \right)}}{\sec^{4}{\left(2 x - \frac{\pi}{2} \right)}}

                             8           
 15*cos(5*x)          320*sin (2*x)      
-------------- + ------------------------
1 + 3*sin(5*x)                     4     
                 (1 + cos(4*x))*sin (4*x)

\frac{320 \sin^{8}{\left(2 x \right)}}{\left(\cos{\left(4 x \right)} + 1\right) \sin^{4}{\left(4 x \right)}} + \frac{15 \cos{\left(5 x \right)}}{3 \sin{\left(5 x \right)} + 1}

       6                                     
 10*sec (2*x)                 15             
-------------- + ----------------------------
   4/pi      \   /          3      \         
sec |-- - 2*x|   |1 + -------------|*sec(5*x)
    \2       /   |       /      pi\|         
                 |    sec|5*x - --||         
                 \       \      2 //

\frac{10 \sec^{6}{\left(2 x \right)}}{\sec^{4}{\left(- 2 x + \frac{\pi}{2} \right)}} + \frac{15}{\left(1 + \frac{3}{\sec{\left(5 x - \frac{\pi}{2} \right)}}\right) \sec{\left(5 x \right)}}

   /         2/5*x\\                           
15*|1 - 2*sin |---||               8           
   \          \ 2 //        160*sin (2*x)      
-------------------- + ------------------------
   1 + 3*sin(5*x)         4         2/pi      \
                       sin (4*x)*sin |-- + 2*x|
                                     \2       /

\frac{15 \left(1 - 2 \sin^{2}{\left(\frac{5 x}{2} \right)}\right)}{3 \sin{\left(5 x \right)} + 1} + \frac{160 \sin^{8}{\left(2 x \right)}}{\sin^{4}{\left(4 x \right)} \sin^{2}{\left(2 x + \frac{\pi}{2} \right)}}

15*(1 - 2*sin(5*x/2)^2)/(1 + 3*sin(5*x)) + 160*sin(2*x)^8/(sin(4*x)^4*sin(pi/2 + 2*x)^2)

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¿Cómo vas a descomponer esta tan(2*x)^4*(10+10*tan(2*x)^2)+15*cos(5*x)/(1+3*sin(5*x)) expresión en fracciones?

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¿Cómo vas a descomponer esta tan(2x)^4(10+10tan(2x)^2)+15cos(5x)/(1+3sin(5x)) expresión en fracciones?