Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
-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))
¿Cómo vas a descomponer esta -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)) expresión en fracciones?
Solución
Ha introducido
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-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
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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
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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
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/ 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
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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
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/ 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
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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
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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)
Denominador común
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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)