Descomposición de una fracción -10*sin(x)/(63*cos(x)⁷)+sin(x)/(9*cos(x)⁹)+sin(x)/(105*cos(x)⁵)+4*sin(x)/(315*cos(x)³)+8*sin(x)/(315*cos(x)) (menos 10 multiplicar por seno de (x) dividir por (63 multiplicar por coseno de (x) en el grado 7) más seno de (x) dividir por (9 multiplicar por coseno de (x) en el grado 9) más seno de (x) dividir por (105 multiplicar por coseno de (x) en el grado 5) más 4 multiplicar por seno de (x) dividir por (315 multiplicar por coseno de (x) al cubo) más 8 multiplicar por seno de (x) dividir por (315 multiplicar por coseno de (x)))

Ha introducido [src]

-10*sin(x)     sin(x)       sin(x)       4*sin(x)     8*sin(x) 
---------- + --------- + ----------- + ----------- + ----------
      7           9             5             3      315*cos(x)
63*cos (x)   9*cos (x)   105*cos (x)   315*cos (x)

\left(\left(\left(\frac{\left(-1\right) 10 \sin{\left(x \right)}}{63 \cos^{7}{\left(x \right)}} + \frac{\sin{\left(x \right)}}{9 \cos^{9}{\left(x \right)}}\right) + \frac{\sin{\left(x \right)}}{105 \cos^{5}{\left(x \right)}}\right) + \frac{4 \sin{\left(x \right)}}{315 \cos^{3}{\left(x \right)}}\right) + \frac{8 \sin{\left(x \right)}}{315 \cos{\left(x \right)}}

(-10*sin(x))/((63*cos(x)^7)) + sin(x)/((9*cos(x)^9)) + sin(x)/((105*cos(x)^5)) + (4*sin(x))/((315*cos(x)^3)) + (8*sin(x))/((315*cos(x)))

Simplificación general [src]

   5    /           2           4   \
sin (x)*\63 - 36*sin (x) + 8*sin (x)/
-------------------------------------
                    9                
             315*cos (x)

\frac{\left(8 \sin^{4}{\left(x \right)} - 36 \sin^{2}{\left(x \right)} + 63\right) \sin^{5}{\left(x \right)}}{315 \cos^{9}{\left(x \right)}}

sin(x)^5*(63 - 36*sin(x)^2 + 8*sin(x)^4)/(315*cos(x)^9)

Respuesta numérica [src]

0.00952380952380952*sin(x)/cos(x)^5 + 0.111111111111111*sin(x)/cos(x)^9 + 0.0126984126984127*sin(x)/cos(x)^3 + 0.0253968253968254*sin(x)/cos(x) - 0.158730158730159*sin(x)/cos(x)^7

0.00952380952380952*sin(x)/cos(x)^5 + 0.111111111111111*sin(x)/cos(x)^9 + 0.0126984126984127*sin(x)/cos(x)^3 + 0.0253968253968254*sin(x)/cos(x) - 0.158730158730159*sin(x)/cos(x)^7

Denominador racional [src]

    /       3    /       5    /        9                   7          \          16          \             21          \                       24          
315*\315*cos (x)*\105*cos (x)*\- 90*cos (x)*sin(x) + 63*cos (x)*sin(x)/ + 567*cos  (x)*sin(x)/ + 238140*cos  (x)*sin(x)/*cos(x) + 150028200*cos  (x)*sin(x)
-----------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                  25                                                                       
                                                                    5907360375*cos  (x)

\frac{315 \left(315 \left(105 \left(- 90 \sin{\left(x \right)} \cos^{9}{\left(x \right)} + 63 \sin{\left(x \right)} \cos^{7}{\left(x \right)}\right) \cos^{5}{\left(x \right)} + 567 \sin{\left(x \right)} \cos^{16}{\left(x \right)}\right) \cos^{3}{\left(x \right)} + 238140 \sin{\left(x \right)} \cos^{21}{\left(x \right)}\right) \cos{\left(x \right)} + 150028200 \sin{\left(x \right)} \cos^{24}{\left(x \right)}}{5907360375 \cos^{25}{\left(x \right)}}

(315*(315*cos(x)^3*(105*cos(x)^5*(-90*cos(x)^9*sin(x) + 63*cos(x)^7*sin(x)) + 567*cos(x)^16*sin(x)) + 238140*cos(x)^21*sin(x))*cos(x) + 150028200*cos(x)^24*sin(x))/(5907360375*cos(x)^25)

Combinatoria [src]

            2              2 /          4            2   \       
(1 + cos(x)) *(-1 + cos(x)) *\35 + 8*cos (x) + 20*cos (x)/*sin(x)
-----------------------------------------------------------------
                                  9                              
                           315*cos (x)

\frac{\left(\cos{\left(x \right)} - 1\right)^{2} \left(\cos{\left(x \right)} + 1\right)^{2} \left(8 \cos^{4}{\left(x \right)} + 20 \cos^{2}{\left(x \right)} + 35\right) \sin{\left(x \right)}}{315 \cos^{9}{\left(x \right)}}

(1 + cos(x))^2*(-1 + cos(x))^2*(35 + 8*cos(x)^4 + 20*cos(x)^2)*sin(x)/(315*cos(x)^9)

Unión de expresiones racionales [src]

/           2           4           6           8   \       
\35 - 50*cos (x) + 3*cos (x) + 4*cos (x) + 8*cos (x)/*sin(x)
------------------------------------------------------------
                               9                            
                        315*cos (x)

\frac{\left(8 \cos^{8}{\left(x \right)} + 4 \cos^{6}{\left(x \right)} + 3 \cos^{4}{\left(x \right)} - 50 \cos^{2}{\left(x \right)} + 35\right) \sin{\left(x \right)}}{315 \cos^{9}{\left(x \right)}}

(35 - 50*cos(x)^2 + 3*cos(x)^4 + 4*cos(x)^6 + 8*cos(x)^8)*sin(x)/(315*cos(x)^9)

Compilar la expresión [src]

  10*sin(x)      sin(x)       sin(x)       4*sin(x)     8*sin(x) 
- ---------- + --------- + ----------- + ----------- + ----------
        7           9             5             3      315*cos(x)
  63*cos (x)   9*cos (x)   105*cos (x)   315*cos (x)

\frac{8 \sin{\left(x \right)}}{315 \cos{\left(x \right)}} + \frac{4 \sin{\left(x \right)}}{315 \cos^{3}{\left(x \right)}} + \frac{\sin{\left(x \right)}}{105 \cos^{5}{\left(x \right)}} - \frac{10 \sin{\left(x \right)}}{63 \cos^{7}{\left(x \right)}} + \frac{\sin{\left(x \right)}}{9 \cos^{9}{\left(x \right)}}

-10*sin(x)/(63*cos(x)^7) + sin(x)/(9*cos(x)^9) + sin(x)/(105*cos(x)^5) + 4*sin(x)/(315*cos(x)^3) + 8*sin(x)/(315*cos(x))

Potencias [src]

  10*sin(x)      sin(x)       sin(x)       4*sin(x)     8*sin(x) 
- ---------- + --------- + ----------- + ----------- + ----------
        7           9             5             3      315*cos(x)
  63*cos (x)   9*cos (x)   105*cos (x)   315*cos (x)

\frac{8 \sin{\left(x \right)}}{315 \cos{\left(x \right)}} + \frac{4 \sin{\left(x \right)}}{315 \cos^{3}{\left(x \right)}} + \frac{\sin{\left(x \right)}}{105 \cos^{5}{\left(x \right)}} - \frac{10 \sin{\left(x \right)}}{63 \cos^{7}{\left(x \right)}} + \frac{\sin{\left(x \right)}}{9 \cos^{9}{\left(x \right)}}

      /   -I*x    I*x\       /   -I*x    I*x\     /   -I*x    I*x\      /   -I*x    I*x\       /   -I*x    I*x\
  4*I*\- e     + e   /   2*I*\- e     + e   /   I*\- e     + e   /    I*\- e     + e   /   5*I*\- e     + e   /
- -------------------- - -------------------- - ------------------ - ------------------- + --------------------
       I*x        -I*x                     3                     9                     5                     7 
  315*e      315*e           / I*x    -I*x\        / I*x    -I*x\        / I*x    -I*x\        / I*x    -I*x\  
  -------- + ---------       |e      e    |        |e      e    |        |e      e    |        |e      e    |  
     2           2       315*|---- + -----|     18*|---- + -----|    210*|---- + -----|     63*|---- + -----|  
                             \ 2       2  /        \ 2       2  /        \ 2       2  /        \ 2       2  /

- \frac{4 i \left(e^{i x} - e^{- i x}\right)}{\frac{315 e^{i x}}{2} + \frac{315 e^{- i x}}{2}} - \frac{2 i \left(e^{i x} - e^{- i x}\right)}{315 \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)^{3}} - \frac{i \left(e^{i x} - e^{- i x}\right)}{210 \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)^{5}} + \frac{5 i \left(e^{i x} - e^{- i x}\right)}{63 \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)^{7}} - \frac{i \left(e^{i x} - e^{- i x}\right)}{18 \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)^{9}}

-4*i*(-exp(-i*x) + exp(i*x))/(315*exp(i*x)/2 + 315*exp(-i*x)/2) - 2*i*(-exp(-i*x) + exp(i*x))/(315*(exp(i*x)/2 + exp(-i*x)/2)^3) - i*(-exp(-i*x) + exp(i*x))/(18*(exp(i*x)/2 + exp(-i*x)/2)^9) - i*(-exp(-i*x) + exp(i*x))/(210*(exp(i*x)/2 + exp(-i*x)/2)^5) + 5*i*(-exp(-i*x) + exp(i*x))/(63*(exp(i*x)/2 + exp(-i*x)/2)^7)

Abrimos la expresión [src]

  10*sin(x)      sin(x)       sin(x)       4*sin(x)     8*sin(x) 
- ---------- + --------- + ----------- + ----------- + ----------
        7           9             5             3      315*cos(x)
  63*cos (x)   9*cos (x)   105*cos (x)   315*cos (x)

\frac{8 \sin{\left(x \right)}}{315 \cos{\left(x \right)}} + \frac{4 \sin{\left(x \right)}}{315 \cos^{3}{\left(x \right)}} + \frac{\sin{\left(x \right)}}{105 \cos^{5}{\left(x \right)}} - \frac{10 \sin{\left(x \right)}}{63 \cos^{7}{\left(x \right)}} + \frac{\sin{\left(x \right)}}{9 \cos^{9}{\left(x \right)}}

-10*sin(x)/(63*cos(x)^7) + sin(x)/(9*cos(x)^9) + sin(x)/(105*cos(x)^5) + 4*sin(x)/(315*cos(x)^3) + 8*sin(x)/(315*cos(x))

Denominador común [src]

                  2                  4                  6                  8          
35*sin(x) - 50*cos (x)*sin(x) + 3*cos (x)*sin(x) + 4*cos (x)*sin(x) + 8*cos (x)*sin(x)
--------------------------------------------------------------------------------------
                                            9                                         
                                     315*cos (x)

\frac{8 \sin{\left(x \right)} \cos^{8}{\left(x \right)} + 4 \sin{\left(x \right)} \cos^{6}{\left(x \right)} + 3 \sin{\left(x \right)} \cos^{4}{\left(x \right)} - 50 \sin{\left(x \right)} \cos^{2}{\left(x \right)} + 35 \sin{\left(x \right)}}{315 \cos^{9}{\left(x \right)}}

(35*sin(x) - 50*cos(x)^2*sin(x) + 3*cos(x)^4*sin(x) + 4*cos(x)^6*sin(x) + 8*cos(x)^8*sin(x))/(315*cos(x)^9)

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