Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
log(z)*(-2)+2*c^i*2*z-1/(2*z^2)+cos(2*z)/((2*z^2))-sin(2*z)/z+log(z^2)
¿Cómo vas a descomponer esta log(z)*(-2)+2*c^i*2*z-1/(2*z^2)+cos(2*z)/((2*z^2))-sin(2*z)/z+log(z^2) expresión en fracciones?
Solución
Ha introducido
[src]
I 1 cos(2*z) sin(2*z) / 2\
log(z)*(-2) + 2*c *2*z - ---- + -------- - -------- + log\z /
2 2 z
2*z 2*z
$$\left(\left(\left(\left(z 2 \cdot 2 c^{i} + \left(-2\right) \log{\left(z \right)}\right) - \frac{1}{2 z^{2}}\right) + \frac{\cos{\left(2 z \right)}}{2 z^{2}}\right) - \frac{\sin{\left(2 z \right)}}{z}\right) + \log{\left(z^{2} \right)}$$
log(z)*(-2) + ((2*c^i)*2)*z - 1/(2*z^2) + cos(2*z)/((2*z^2)) - sin(2*z)/z + log(z^2)
Simplificación general
[src]
1 cos(2*z) sin(2*z) I / 2\
-2*log(z) - ---- + -------- - -------- + 4*z*c + log\z /
2 2 z
2*z 2*z
$$4 c^{i} z - 2 \log{\left(z \right)} + \log{\left(z^{2} \right)} - \frac{\sin{\left(2 z \right)}}{z} + \frac{\cos{\left(2 z \right)}}{2 z^{2}} - \frac{1}{2 z^{2}}$$
-2*log(z) - 1/(2*z^2) + cos(2*z)/(2*z^2) - sin(2*z)/z + 4*z*c^i + log(z^2)
Respuesta numérica
[src]
-0.5/z^2 - 2.0*log(z) - sin(2*z)/z + 0.5*cos(2*z)/z^2 + 4.0*z*c^i + log(z^2)
-0.5/z^2 - 2.0*log(z) - sin(2*z)/z + 0.5*cos(2*z)/z^2 + 4.0*z*c^i + log(z^2)
Denominador racional
[src]
/ 2 / I\ \ 2 3 / 2\
z*\-1 + 2*z *\-2*log(z) + 4*z*c / + cos(2*z)/ - 2*z *sin(2*z) + 2*z *log\z /
----------------------------------------------------------------------------
3
2*z
$$\frac{2 z^{3} \log{\left(z^{2} \right)} - 2 z^{2} \sin{\left(2 z \right)} + z \left(2 z^{2} \left(4 c^{i} z - 2 \log{\left(z \right)}\right) + \cos{\left(2 z \right)} - 1\right)}{2 z^{3}}$$
(z*(-1 + 2*z^2*(-2*log(z) + 4*z*c^i) + cos(2*z)) - 2*z^2*sin(2*z) + 2*z^3*log(z^2))/(2*z^3)
Potencias
[src]
1 cos(2*z) sin(2*z) I / 2\
-2*log(z) - ---- + -------- - -------- + 4*z*c + log\z /
2 2 z
2*z 2*z
$$4 c^{i} z - 2 \log{\left(z \right)} + \log{\left(z^{2} \right)} - \frac{\sin{\left(2 z \right)}}{z} + \frac{\cos{\left(2 z \right)}}{2 z^{2}} - \frac{1}{2 z^{2}}$$
-2*I*z 2*I*z
e e
------- + ------ / -2*I*z 2*I*z\
1 2 2 I I*\- e + e / / 2\
-2*log(z) - ---- + ---------------- + 4*z*c + ---------------------- + log\z /
2 2 2*z
2*z 2*z
$$4 c^{i} z - 2 \log{\left(z \right)} + \log{\left(z^{2} \right)} + \frac{i \left(e^{2 i z} - e^{- 2 i z}\right)}{2 z} + \frac{\frac{e^{2 i z}}{2} + \frac{e^{- 2 i z}}{2}}{2 z^{2}} - \frac{1}{2 z^{2}}$$
-2*log(z) - 1/(2*z^2) + (exp(-2*i*z)/2 + exp(2*i*z)/2)/(2*z^2) + 4*z*c^i + i*(-exp(-2*i*z) + exp(2*i*z))/(2*z) + log(z^2)
Unión de expresiones racionales
[src]
2 / 2\ 2 / I\
-1 - 2*z*sin(2*z) + 2*z *log\z / + 4*z *\-log(z) + 2*z*c / + cos(2*z)
---------------------------------------------------------------------
2
2*z
$$\frac{4 z^{2} \left(2 c^{i} z - \log{\left(z \right)}\right) + 2 z^{2} \log{\left(z^{2} \right)} - 2 z \sin{\left(2 z \right)} + \cos{\left(2 z \right)} - 1}{2 z^{2}}$$
(-1 - 2*z*sin(2*z) + 2*z^2*log(z^2) + 4*z^2*(-log(z) + 2*z*c^i) + cos(2*z))/(2*z^2)
Denominador común
[src]
I 1 - cos(2*z) + 2*z*sin(2*z) / 2\
-2*log(z) + 4*z*c - --------------------------- + log\z /
2
2*z
$$4 c^{i} z - 2 \log{\left(z \right)} + \log{\left(z^{2} \right)} - \frac{2 z \sin{\left(2 z \right)} - \cos{\left(2 z \right)} + 1}{2 z^{2}}$$
-2*log(z) + 4*z*c^i - (1 - cos(2*z) + 2*z*sin(2*z))/(2*z^2) + log(z^2)
Combinatoria
[src]
2 2 / 2\ I 3
-1 - 4*z *log(z) - 2*z*sin(2*z) + 2*z *log\z / + 8*c *z + cos(2*z)
-------------------------------------------------------------------
2
2*z
$$\frac{8 c^{i} z^{3} - 4 z^{2} \log{\left(z \right)} + 2 z^{2} \log{\left(z^{2} \right)} - 2 z \sin{\left(2 z \right)} + \cos{\left(2 z \right)} - 1}{2 z^{2}}$$
(-1 - 4*z^2*log(z) - 2*z*sin(2*z) + 2*z^2*log(z^2) + 8*c^i*z^3 + cos(2*z))/(2*z^2)
Compilar la expresión
[src]
1 cos(2*z)
- - + --------
2 2 sin(2*z) I / 2\
-2*log(z) + -------------- - -------- + 4*z*c + log\z /
2 z
z
$$4 c^{i} z - 2 \log{\left(z \right)} + \log{\left(z^{2} \right)} - \frac{\sin{\left(2 z \right)}}{z} + \frac{\frac{\cos{\left(2 z \right)}}{2} - \frac{1}{2}}{z^{2}}$$
1 cos(2*z) sin(2*z) I / 2\
-2*log(z) - ---- + -------- - -------- + 4*z*c + log\z /
2 2 z
2*z 2*z
$$4 c^{i} z - 2 \log{\left(z \right)} + \log{\left(z^{2} \right)} - \frac{\sin{\left(2 z \right)}}{z} + \frac{\cos{\left(2 z \right)}}{2 z^{2}} - \frac{1}{2 z^{2}}$$
-2*log(z) - 1/(2*z^2) + cos(2*z)/(2*z^2) - sin(2*z)/z + 4*z*c^i + log(z^2)
Parte trigonométrica
[src]
/pi \
sin|-- + 2*z|
1 \2 / sin(2*z) I / 2\
-2*log(z) - ---- + ------------- - -------- + 4*z*c + log\z /
2 2 z
2*z 2*z
$$4 c^{i} z - 2 \log{\left(z \right)} + \log{\left(z^{2} \right)} - \frac{\sin{\left(2 z \right)}}{z} + \frac{\sin{\left(2 z + \frac{\pi}{2} \right)}}{2 z^{2}} - \frac{1}{2 z^{2}}$$
2
sin(2*z) sin (z) I / 2\
-2*log(z) - -------- - ------- + 4*z*c + log\z /
z 2
z
$$4 c^{i} z - 2 \log{\left(z \right)} + \log{\left(z^{2} \right)} - \frac{\sin{\left(2 z \right)}}{z} - \frac{\sin^{2}{\left(z \right)}}{z^{2}}$$
1 1 1 I / 2\
-2*log(z) - ---- + ------------- - --------------- + 4*z*c + log\z /
2 2 / pi\
2*z 2*z *sec(2*z) z*sec|2*z - --|
\ 2 /
$$4 c^{i} z - 2 \log{\left(z \right)} + \log{\left(z^{2} \right)} - \frac{1}{z \sec{\left(2 z - \frac{\pi}{2} \right)}} - \frac{1}{2 z^{2}} + \frac{1}{2 z^{2} \sec{\left(2 z \right)}}$$
/ pi\
cos|2*z - --|
1 cos(2*z) \ 2 / I / 2\
-2*log(z) - ---- + -------- - ------------- + 4*z*c + log\z /
2 2 z
2*z 2*z
$$4 c^{i} z - 2 \log{\left(z \right)} + \log{\left(z^{2} \right)} - \frac{\cos{\left(2 z - \frac{\pi}{2} \right)}}{z} + \frac{\cos{\left(2 z \right)}}{2 z^{2}} - \frac{1}{2 z^{2}}$$
1 1 1 I / 2\
-2*log(z) - ---- + ------------- - ---------- + 4*z*c + log\z /
2 2 z*csc(2*z)
2*z 2*z *sec(2*z)
$$4 c^{i} z - 2 \log{\left(z \right)} + \log{\left(z^{2} \right)} - \frac{1}{z \csc{\left(2 z \right)}} - \frac{1}{2 z^{2}} + \frac{1}{2 z^{2} \sec{\left(2 z \right)}}$$
2
1 I -1 + cot (z) 2*cot(z) / 2\
-2*log(z) - ---- + 4*z*c + ------------------ - --------------- + log\z /
2 2 / 2 \ / 2 \
2*z 2*z *\1 + cot (z)/ z*\1 + cot (z)/
$$4 c^{i} z - 2 \log{\left(z \right)} + \log{\left(z^{2} \right)} - \frac{2 \cot{\left(z \right)}}{z \left(\cot^{2}{\left(z \right)} + 1\right)} + \frac{\cot^{2}{\left(z \right)} - 1}{2 z^{2} \left(\cot^{2}{\left(z \right)} + 1\right)} - \frac{1}{2 z^{2}}$$
2
1 I 1 - tan (z) 2*tan(z) / 2\
-2*log(z) - ---- + 4*z*c + ------------------ - --------------- + log\z /
2 2 / 2 \ / 2 \
2*z 2*z *\1 + tan (z)/ z*\1 + tan (z)/
$$4 c^{i} z - 2 \log{\left(z \right)} + \log{\left(z^{2} \right)} - \frac{2 \tan{\left(z \right)}}{z \left(\tan^{2}{\left(z \right)} + 1\right)} + \frac{1 - \tan^{2}{\left(z \right)}}{2 z^{2} \left(\tan^{2}{\left(z \right)} + 1\right)} - \frac{1}{2 z^{2}}$$
1 cos(2*z) sin(2*z) I / 2\
-2*log(z) - ---- + -------- - -------- + 4*z*c + log\z /
2 2 z
2*z 2*z
$$4 c^{i} z - 2 \log{\left(z \right)} + \log{\left(z^{2} \right)} - \frac{\sin{\left(2 z \right)}}{z} + \frac{\cos{\left(2 z \right)}}{2 z^{2}} - \frac{1}{2 z^{2}}$$
1 1 1 I / 2\
-2*log(z) - ---- + ------------------ - ---------- + 4*z*c + log\z /
2 2 /pi \ z*csc(2*z)
2*z 2*z *csc|-- - 2*z|
\2 /
$$4 c^{i} z - 2 \log{\left(z \right)} + \log{\left(z^{2} \right)} - \frac{1}{z \csc{\left(2 z \right)}} - \frac{1}{2 z^{2}} + \frac{1}{2 z^{2} \csc{\left(- 2 z + \frac{\pi}{2} \right)}}$$
-2*log(z) - 1/(2*z^2) + 1/(2*z^2*csc(pi/2 - 2*z)) - 1/(z*csc(2*z)) + 4*z*c^i + log(z^2)