Simplificación general
[src]
1 3 sin(2*x) 3 cos(4*x)
- + cos (x) + -------- - sin (x) - --------
8 2 8
-------------------------------------------
/ sin(2*x)\ 2
|1 + --------|*cos (x)
\ 2 /
$$\frac{- \sin^{3}{\left(x \right)} + \frac{\sin{\left(2 x \right)}}{2} + \cos^{3}{\left(x \right)} - \frac{\cos{\left(4 x \right)}}{8} + \frac{1}{8}}{\left(\frac{\sin{\left(2 x \right)}}{2} + 1\right) \cos^{2}{\left(x \right)}}$$
(1/8 + cos(x)^3 + sin(2*x)/2 - sin(x)^3 - cos(4*x)/8)/((1 + sin(2*x)/2)*cos(x)^2)
(cos(x)^3 - sin(x)^3)/((1.0 + cos(x)*sin(x))*cos(x)^2) + tan(x)
(cos(x)^3 - sin(x)^3)/((1.0 + cos(x)*sin(x))*cos(x)^2) + tan(x)
3 3
cos (x) - sin (x)
------------------------ + tan(x)
2 3
cos (x) + cos (x)*sin(x)
$$\tan{\left(x \right)} + \frac{- \sin^{3}{\left(x \right)} + \cos^{3}{\left(x \right)}}{\sin{\left(x \right)} \cos^{3}{\left(x \right)} + \cos^{2}{\left(x \right)}}$$
(cos(x)^3 - sin(x)^3)/(cos(x)^2 + cos(x)^3*sin(x)) + tan(x)
Denominador racional
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3 3 2
cos (x) - sin (x) + cos (x)*(1 + cos(x)*sin(x))*tan(x)
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2
(1 + cos(x)*sin(x))*cos (x)
$$\frac{\left(\sin{\left(x \right)} \cos{\left(x \right)} + 1\right) \cos^{2}{\left(x \right)} \tan{\left(x \right)} - \sin^{3}{\left(x \right)} + \cos^{3}{\left(x \right)}}{\left(\sin{\left(x \right)} \cos{\left(x \right)} + 1\right) \cos^{2}{\left(x \right)}}$$
(cos(x)^3 - sin(x)^3 + cos(x)^2*(1 + cos(x)*sin(x))*tan(x))/((1 + cos(x)*sin(x))*cos(x)^2)
3 3 2 3
cos (x) - sin (x) + cos (x)*tan(x) + cos (x)*sin(x)*tan(x)
----------------------------------------------------------
2
(1 + cos(x)*sin(x))*cos (x)
$$\frac{- \sin^{3}{\left(x \right)} + \sin{\left(x \right)} \cos^{3}{\left(x \right)} \tan{\left(x \right)} + \cos^{3}{\left(x \right)} + \cos^{2}{\left(x \right)} \tan{\left(x \right)}}{\left(\sin{\left(x \right)} \cos{\left(x \right)} + 1\right) \cos^{2}{\left(x \right)}}$$
(cos(x)^3 - sin(x)^3 + cos(x)^2*tan(x) + cos(x)^3*sin(x)*tan(x))/((1 + cos(x)*sin(x))*cos(x)^2)
3 3
/ I*x -I*x\ / -I*x I*x\
|e e | I*\- e + e /
/ I*x -I*x\ |---- + -----| - -------------------
I*\- e + e / \ 2 2 / 8
------------------ + -------------------------------------------------------
I*x -I*x / / I*x -I*x\ \
e + e | |e e | / -I*x I*x\| 2
| I*|---- + -----|*\- e + e /| / I*x -I*x\
| \ 2 2 / | |e e |
|1 - ---------------------------------|*|---- + -----|
\ 2 / \ 2 2 /
$$\frac{i \left(- e^{i x} + e^{- i x}\right)}{e^{i x} + e^{- i x}} + \frac{\left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)^{3} - \frac{i \left(e^{i x} - e^{- i x}\right)^{3}}{8}}{\left(- \frac{i \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right) \left(e^{i x} - e^{- i x}\right)}{2} + 1\right) \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)^{2}}$$
i*(-exp(i*x) + exp(-i*x))/(exp(i*x) + exp(-i*x)) + ((exp(i*x)/2 + exp(-i*x)/2)^3 - i*(-exp(-i*x) + exp(i*x))^3/8)/((1 - i*(exp(i*x)/2 + exp(-i*x)/2)*(-exp(-i*x) + exp(i*x))/2)*(exp(i*x)/2 + exp(-i*x)/2)^2)
Unión de expresiones racionales
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3 3 2
cos (x) - sin (x) + cos (x)*(1 + cos(x)*sin(x))*tan(x)
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2
(1 + cos(x)*sin(x))*cos (x)
$$\frac{\left(\sin{\left(x \right)} \cos{\left(x \right)} + 1\right) \cos^{2}{\left(x \right)} \tan{\left(x \right)} - \sin^{3}{\left(x \right)} + \cos^{3}{\left(x \right)}}{\left(\sin{\left(x \right)} \cos{\left(x \right)} + 1\right) \cos^{2}{\left(x \right)}}$$
(cos(x)^3 - sin(x)^3 + cos(x)^2*(1 + cos(x)*sin(x))*tan(x))/((1 + cos(x)*sin(x))*cos(x)^2)
Abrimos la expresión
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3 3
cos (x) sin (x)
------------------------ - ------------------------ + tan(x)
2 3 2 3
cos (x) + cos (x)*sin(x) cos (x) + cos (x)*sin(x)
$$\tan{\left(x \right)} - \frac{\sin^{3}{\left(x \right)}}{\sin{\left(x \right)} \cos^{3}{\left(x \right)} + \cos^{2}{\left(x \right)}} + \frac{\cos^{3}{\left(x \right)}}{\sin{\left(x \right)} \cos^{3}{\left(x \right)} + \cos^{2}{\left(x \right)}}$$
cos(x)^3/(cos(x)^2 + cos(x)^3*sin(x)) - sin(x)^3/(cos(x)^2 + cos(x)^3*sin(x)) + tan(x)