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Expresiones semejantes
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Expresiones con funciones
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- Coseno cos
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- cos2x+2(sqrt2)sin((pi/2)+x)-2=0
- cos(0,895+0,45)-1,2=x
- cos(x)-cos3x=sin(x)
- cos(5*x)^2=4
cos(x)*(cos(x)+a)^2=1 la ecuación
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Solución
Ha introducido
[src]
2 cos(x)*(cos(x) + a) = 1
$$\left(a + \cos{\left(x \right)}\right)^{2} \cos{\left(x \right)} = 1$$
Gráfica
Respuesta rápida
[src]
/ / ________________________________________ \\ / / ________________________________________ \\
| | / ______________________ || | | / ______________________ ||
| | / / 2 || | | / / 2 ||
| | / / / 3\ 6 || | | / / / 3\ 6 ||
| | / 27 \/ \-27 - 2*a / - 4*a 3 || | | / 27 \/ \-27 - 2*a / - 4*a 3 ||
| | 3 / - -- + -------------------------- - a 2 || | | 3 / - -- + -------------------------- - a 2 ||
| | 2*a \/ 2 2 a || | | 2*a \/ 2 2 a ||
x1 = - re|acos|- --- - ----------------------------------------------- - -------------------------------------------------|| + 2*pi - I*im|acos|- --- - ----------------------------------------------- - -------------------------------------------------||
| | 3 3 ________________________________________|| | | 3 3 ________________________________________||
| | / ______________________ || | | / ______________________ ||
| | / / 2 || | | / / 2 ||
| | / / / 3\ 6 || | | / / / 3\ 6 ||
| | / 27 \/ \-27 - 2*a / - 4*a 3 || | | / 27 \/ \-27 - 2*a / - 4*a 3 ||
| | 3*3 / - -- + -------------------------- - a || | | 3*3 / - -- + -------------------------- - a ||
\ \ \/ 2 2 // \ \ \/ 2 2 //
$$x_{1} = - \operatorname{re}{\left(\operatorname{acos}{\left(- \frac{a^{2}}{3 \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}} - \frac{2 a}{3} - \frac{\sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}}{3} \right)}\right)} - i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{a^{2}}{3 \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}} - \frac{2 a}{3} - \frac{\sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}}{3} \right)}\right)} + 2 \pi$$
/ / ________________________________________ \\ / / ________________________________________ \\
| | / ______________________ || | | / ______________________ ||
| | / / 2 || | | / / 2 ||
| | / / / 3\ 6 / ___\ || | | / / / 3\ 6 / ___\ ||
| | / 27 \/ \-27 - 2*a / - 4*a 3 | 1 I*\/ 3 | || | | / 27 \/ \-27 - 2*a / - 4*a 3 | 1 I*\/ 3 | ||
| | 3 / - -- + -------------------------- - a *|- - - -------| 2 || | | 3 / - -- + -------------------------- - a *|- - - -------| 2 ||
| | 2*a \/ 2 2 \ 2 2 / a || | | 2*a \/ 2 2 \ 2 2 / a ||
x2 = - re|acos|- --- - --------------------------------------------------------------- - -----------------------------------------------------------------|| + 2*pi - I*im|acos|- --- - --------------------------------------------------------------- - -----------------------------------------------------------------||
| | 3 3 ________________________________________|| | | 3 3 ________________________________________||
| | / ______________________ || | | / ______________________ ||
| | / / 2 || | | / / 2 ||
| | / ___\ / / / 3\ 6 || | | / ___\ / / / 3\ 6 ||
| | | 1 I*\/ 3 | / 27 \/ \-27 - 2*a / - 4*a 3 || | | | 1 I*\/ 3 | / 27 \/ \-27 - 2*a / - 4*a 3 ||
| | 3*|- - - -------|*3 / - -- + -------------------------- - a || | | 3*|- - - -------|*3 / - -- + -------------------------- - a ||
\ \ \ 2 2 / \/ 2 2 // \ \ \ 2 2 / \/ 2 2 //
$$x_{2} = - \operatorname{re}{\left(\operatorname{acos}{\left(- \frac{a^{2}}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}} - \frac{2 a}{3} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}}{3} \right)}\right)} - i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{a^{2}}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}} - \frac{2 a}{3} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}}{3} \right)}\right)} + 2 \pi$$
/ / ________________________________________ \\ / / ________________________________________ \\
| | / ______________________ || | | / ______________________ ||
| | / / 2 || | | / / 2 ||
| | / / / 3\ 6 / ___\ || | | / / / 3\ 6 / ___\ ||
| | / 27 \/ \-27 - 2*a / - 4*a 3 | 1 I*\/ 3 | || | | / 27 \/ \-27 - 2*a / - 4*a 3 | 1 I*\/ 3 | ||
| | 3 / - -- + -------------------------- - a *|- - + -------| 2 || | | 3 / - -- + -------------------------- - a *|- - + -------| 2 ||
| | 2*a \/ 2 2 \ 2 2 / a || | | 2*a \/ 2 2 \ 2 2 / a ||
x3 = - re|acos|- --- - --------------------------------------------------------------- - -----------------------------------------------------------------|| + 2*pi - I*im|acos|- --- - --------------------------------------------------------------- - -----------------------------------------------------------------||
| | 3 3 ________________________________________|| | | 3 3 ________________________________________||
| | / ______________________ || | | / ______________________ ||
| | / / 2 || | | / / 2 ||
| | / ___\ / / / 3\ 6 || | | / ___\ / / / 3\ 6 ||
| | | 1 I*\/ 3 | / 27 \/ \-27 - 2*a / - 4*a 3 || | | | 1 I*\/ 3 | / 27 \/ \-27 - 2*a / - 4*a 3 ||
| | 3*|- - + -------|*3 / - -- + -------------------------- - a || | | 3*|- - + -------|*3 / - -- + -------------------------- - a ||
\ \ \ 2 2 / \/ 2 2 // \ \ \ 2 2 / \/ 2 2 //
$$x_{3} = - \operatorname{re}{\left(\operatorname{acos}{\left(- \frac{a^{2}}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}} - \frac{2 a}{3} - \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}}{3} \right)}\right)} - i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{a^{2}}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}} - \frac{2 a}{3} - \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}}{3} \right)}\right)} + 2 \pi$$
/ / ________________________________________ \\ / / ________________________________________ \\
| | / ______________________ || | | / ______________________ ||
| | / / 2 || | | / / 2 ||
| | / / / 3\ 6 || | | / / / 3\ 6 ||
| | / 27 \/ \-27 - 2*a / - 4*a 3 || | | / 27 \/ \-27 - 2*a / - 4*a 3 ||
| | 3 / - -- + -------------------------- - a 2 || | | 3 / - -- + -------------------------- - a 2 ||
| | 2*a \/ 2 2 a || | | 2*a \/ 2 2 a ||
x4 = I*im|acos|- --- - ----------------------------------------------- - -------------------------------------------------|| + re|acos|- --- - ----------------------------------------------- - -------------------------------------------------||
| | 3 3 ________________________________________|| | | 3 3 ________________________________________||
| | / ______________________ || | | / ______________________ ||
| | / / 2 || | | / / 2 ||
| | / / / 3\ 6 || | | / / / 3\ 6 ||
| | / 27 \/ \-27 - 2*a / - 4*a 3 || | | / 27 \/ \-27 - 2*a / - 4*a 3 ||
| | 3*3 / - -- + -------------------------- - a || | | 3*3 / - -- + -------------------------- - a ||
\ \ \/ 2 2 // \ \ \/ 2 2 //
$$x_{4} = \operatorname{re}{\left(\operatorname{acos}{\left(- \frac{a^{2}}{3 \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}} - \frac{2 a}{3} - \frac{\sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{a^{2}}{3 \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}} - \frac{2 a}{3} - \frac{\sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}}{3} \right)}\right)}$$
/ / ________________________________________ \\ / / ________________________________________ \\
| | / ______________________ || | | / ______________________ ||
| | / / 2 || | | / / 2 ||
| | / / / 3\ 6 / ___\ || | | / / / 3\ 6 / ___\ ||
| | / 27 \/ \-27 - 2*a / - 4*a 3 | 1 I*\/ 3 | || | | / 27 \/ \-27 - 2*a / - 4*a 3 | 1 I*\/ 3 | ||
| | 3 / - -- + -------------------------- - a *|- - - -------| 2 || | | 3 / - -- + -------------------------- - a *|- - - -------| 2 ||
| | 2*a \/ 2 2 \ 2 2 / a || | | 2*a \/ 2 2 \ 2 2 / a ||
x5 = I*im|acos|- --- - --------------------------------------------------------------- - -----------------------------------------------------------------|| + re|acos|- --- - --------------------------------------------------------------- - -----------------------------------------------------------------||
| | 3 3 ________________________________________|| | | 3 3 ________________________________________||
| | / ______________________ || | | / ______________________ ||
| | / / 2 || | | / / 2 ||
| | / ___\ / / / 3\ 6 || | | / ___\ / / / 3\ 6 ||
| | | 1 I*\/ 3 | / 27 \/ \-27 - 2*a / - 4*a 3 || | | | 1 I*\/ 3 | / 27 \/ \-27 - 2*a / - 4*a 3 ||
| | 3*|- - - -------|*3 / - -- + -------------------------- - a || | | 3*|- - - -------|*3 / - -- + -------------------------- - a ||
\ \ \ 2 2 / \/ 2 2 // \ \ \ 2 2 / \/ 2 2 //
$$x_{5} = \operatorname{re}{\left(\operatorname{acos}{\left(- \frac{a^{2}}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}} - \frac{2 a}{3} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{a^{2}}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}} - \frac{2 a}{3} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}}{3} \right)}\right)}$$
/ / ________________________________________ \\ / / ________________________________________ \\
| | / ______________________ || | | / ______________________ ||
| | / / 2 || | | / / 2 ||
| | / / / 3\ 6 / ___\ || | | / / / 3\ 6 / ___\ ||
| | / 27 \/ \-27 - 2*a / - 4*a 3 | 1 I*\/ 3 | || | | / 27 \/ \-27 - 2*a / - 4*a 3 | 1 I*\/ 3 | ||
| | 3 / - -- + -------------------------- - a *|- - + -------| 2 || | | 3 / - -- + -------------------------- - a *|- - + -------| 2 ||
| | 2*a \/ 2 2 \ 2 2 / a || | | 2*a \/ 2 2 \ 2 2 / a ||
x6 = I*im|acos|- --- - --------------------------------------------------------------- - -----------------------------------------------------------------|| + re|acos|- --- - --------------------------------------------------------------- - -----------------------------------------------------------------||
| | 3 3 ________________________________________|| | | 3 3 ________________________________________||
| | / ______________________ || | | / ______________________ ||
| | / / 2 || | | / / 2 ||
| | / ___\ / / / 3\ 6 || | | / ___\ / / / 3\ 6 ||
| | | 1 I*\/ 3 | / 27 \/ \-27 - 2*a / - 4*a 3 || | | | 1 I*\/ 3 | / 27 \/ \-27 - 2*a / - 4*a 3 ||
| | 3*|- - + -------|*3 / - -- + -------------------------- - a || | | 3*|- - + -------|*3 / - -- + -------------------------- - a ||
\ \ \ 2 2 / \/ 2 2 // \ \ \ 2 2 / \/ 2 2 //
$$x_{6} = \operatorname{re}{\left(\operatorname{acos}{\left(- \frac{a^{2}}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}} - \frac{2 a}{3} - \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{a^{2}}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}} - \frac{2 a}{3} - \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}}{3} \right)}\right)}$$
x6 = re(acos(-a^2/(3*(-1/2 + sqrt(3)*i/2)*(-a^3 + sqrt(-4*a^6 + (-2*a^3 - 27)^2)/2 - 27/2)^(1/3)) - 2*a/3 - (-1/2 + sqrt(3)*i/2)*(-a^3 + sqrt(-4*a^6 + (-2*a^3 - 27)^2)/2 - 27/2)^(1/3)/3)) + i*im(acos(-a^2/(3*(-1/2 + sqrt(3)*i/2)*(-a^3 + sqrt(-4*a^6 + (-2*a^3 - 27)^2)/2 - 27/2)^(1/3)) - 2*a/3 - (-1/2 + sqrt(3)*i/2)*(-a^3 + sqrt(-4*a^6 + (-2*a^3 - 27)^2)/2 - 27/2)^(1/3)/3))
Suma y producto de raíces
[src]
suma
/ / ________________________________________ \\ / / ________________________________________ \\ / / ________________________________________ \\ / / ________________________________________ \\ / / ________________________________________ \\ / / ________________________________________ \\ / / ________________________________________ \\ / / ________________________________________ \\ / / ________________________________________ \\ / / ________________________________________ \\ / / ________________________________________ \\ / / ________________________________________ \\
| | / ______________________ || | | / ______________________ || | | / ______________________ || | | / ______________________ || | | / ______________________ || | | / ______________________ || | | / ______________________ || | | / ______________________ || | | / ______________________ || | | / ______________________ || | | / ______________________ || | | / ______________________ ||
| | / / 2 || | | / / 2 || | | / / 2 || | | / / 2 || | | / / 2 || | | / / 2 || | | / / 2 || | | / / 2 || | | / / 2 || | | / / 2 || | | / / 2 || | | / / 2 ||
| | / / / 3\ 6 || | | / / / 3\ 6 || | | / / / 3\ 6 / ___\ || | | / / / 3\ 6 / ___\ || | | / / / 3\ 6 / ___\ || | | / / / 3\ 6 / ___\ || | | / / / 3\ 6 || | | / / / 3\ 6 || | | / / / 3\ 6 / ___\ || | | / / / 3\ 6 / ___\ || | | / / / 3\ 6 / ___\ || | | / / / 3\ 6 / ___\ ||
| | / 27 \/ \-27 - 2*a / - 4*a 3 || | | / 27 \/ \-27 - 2*a / - 4*a 3 || | | / 27 \/ \-27 - 2*a / - 4*a 3 | 1 I*\/ 3 | || | | / 27 \/ \-27 - 2*a / - 4*a 3 | 1 I*\/ 3 | || | | / 27 \/ \-27 - 2*a / - 4*a 3 | 1 I*\/ 3 | || | | / 27 \/ \-27 - 2*a / - 4*a 3 | 1 I*\/ 3 | || | | / 27 \/ \-27 - 2*a / - 4*a 3 || | | / 27 \/ \-27 - 2*a / - 4*a 3 || | | / 27 \/ \-27 - 2*a / - 4*a 3 | 1 I*\/ 3 | || | | / 27 \/ \-27 - 2*a / - 4*a 3 | 1 I*\/ 3 | || | | / 27 \/ \-27 - 2*a / - 4*a 3 | 1 I*\/ 3 | || | | / 27 \/ \-27 - 2*a / - 4*a 3 | 1 I*\/ 3 | ||
| | 3 / - -- + -------------------------- - a 2 || | | 3 / - -- + -------------------------- - a 2 || | | 3 / - -- + -------------------------- - a *|- - - -------| 2 || | | 3 / - -- + -------------------------- - a *|- - - -------| 2 || | | 3 / - -- + -------------------------- - a *|- - + -------| 2 || | | 3 / - -- + -------------------------- - a *|- - + -------| 2 || | | 3 / - -- + -------------------------- - a 2 || | | 3 / - -- + -------------------------- - a 2 || | | 3 / - -- + -------------------------- - a *|- - - -------| 2 || | | 3 / - -- + -------------------------- - a *|- - - -------| 2 || | | 3 / - -- + -------------------------- - a *|- - + -------| 2 || | | 3 / - -- + -------------------------- - a *|- - + -------| 2 ||
| | 2*a \/ 2 2 a || | | 2*a \/ 2 2 a || | | 2*a \/ 2 2 \ 2 2 / a || | | 2*a \/ 2 2 \ 2 2 / a || | | 2*a \/ 2 2 \ 2 2 / a || | | 2*a \/ 2 2 \ 2 2 / a || | | 2*a \/ 2 2 a || | | 2*a \/ 2 2 a || | | 2*a \/ 2 2 \ 2 2 / a || | | 2*a \/ 2 2 \ 2 2 / a || | | 2*a \/ 2 2 \ 2 2 / a || | | 2*a \/ 2 2 \ 2 2 / a ||
- re|acos|- --- - ----------------------------------------------- - -------------------------------------------------|| + 2*pi - I*im|acos|- --- - ----------------------------------------------- - -------------------------------------------------|| + - re|acos|- --- - --------------------------------------------------------------- - -----------------------------------------------------------------|| + 2*pi - I*im|acos|- --- - --------------------------------------------------------------- - -----------------------------------------------------------------|| + - re|acos|- --- - --------------------------------------------------------------- - -----------------------------------------------------------------|| + 2*pi - I*im|acos|- --- - --------------------------------------------------------------- - -----------------------------------------------------------------|| + I*im|acos|- --- - ----------------------------------------------- - -------------------------------------------------|| + re|acos|- --- - ----------------------------------------------- - -------------------------------------------------|| + I*im|acos|- --- - --------------------------------------------------------------- - -----------------------------------------------------------------|| + re|acos|- --- - --------------------------------------------------------------- - -----------------------------------------------------------------|| + I*im|acos|- --- - --------------------------------------------------------------- - -----------------------------------------------------------------|| + re|acos|- --- - --------------------------------------------------------------- - -----------------------------------------------------------------||
| | 3 3 ________________________________________|| | | 3 3 ________________________________________|| | | 3 3 ________________________________________|| | | 3 3 ________________________________________|| | | 3 3 ________________________________________|| | | 3 3 ________________________________________|| | | 3 3 ________________________________________|| | | 3 3 ________________________________________|| | | 3 3 ________________________________________|| | | 3 3 ________________________________________|| | | 3 3 ________________________________________|| | | 3 3 ________________________________________||
| | / ______________________ || | | / ______________________ || | | / ______________________ || | | / ______________________ || | | / ______________________ || | | / ______________________ || | | / ______________________ || | | / ______________________ || | | / ______________________ || | | / ______________________ || | | / ______________________ || | | / ______________________ ||
| | / / 2 || | | / / 2 || | | / / 2 || | | / / 2 || | | / / 2 || | | / / 2 || | | / / 2 || | | / / 2 || | | / / 2 || | | / / 2 || | | / / 2 || | | / / 2 ||
| | / / / 3\ 6 || | | / / / 3\ 6 || | | / ___\ / / / 3\ 6 || | | / ___\ / / / 3\ 6 || | | / ___\ / / / 3\ 6 || | | / ___\ / / / 3\ 6 || | | / / / 3\ 6 || | | / / / 3\ 6 || | | / ___\ / / / 3\ 6 || | | / ___\ / / / 3\ 6 || | | / ___\ / / / 3\ 6 || | | / ___\ / / / 3\ 6 ||
| | / 27 \/ \-27 - 2*a / - 4*a 3 || | | / 27 \/ \-27 - 2*a / - 4*a 3 || | | | 1 I*\/ 3 | / 27 \/ \-27 - 2*a / - 4*a 3 || | | | 1 I*\/ 3 | / 27 \/ \-27 - 2*a / - 4*a 3 || | | | 1 I*\/ 3 | / 27 \/ \-27 - 2*a / - 4*a 3 || | | | 1 I*\/ 3 | / 27 \/ \-27 - 2*a / - 4*a 3 || | | / 27 \/ \-27 - 2*a / - 4*a 3 || | | / 27 \/ \-27 - 2*a / - 4*a 3 || | | | 1 I*\/ 3 | / 27 \/ \-27 - 2*a / - 4*a 3 || | | | 1 I*\/ 3 | / 27 \/ \-27 - 2*a / - 4*a 3 || | | | 1 I*\/ 3 | / 27 \/ \-27 - 2*a / - 4*a 3 || | | | 1 I*\/ 3 | / 27 \/ \-27 - 2*a / - 4*a 3 ||
| | 3*3 / - -- + -------------------------- - a || | | 3*3 / - -- + -------------------------- - a || | | 3*|- - - -------|*3 / - -- + -------------------------- - a || | | 3*|- - - -------|*3 / - -- + -------------------------- - a || | | 3*|- - + -------|*3 / - -- + -------------------------- - a || | | 3*|- - + -------|*3 / - -- + -------------------------- - a || | | 3*3 / - -- + -------------------------- - a || | | 3*3 / - -- + -------------------------- - a || | | 3*|- - - -------|*3 / - -- + -------------------------- - a || | | 3*|- - - -------|*3 / - -- + -------------------------- - a || | | 3*|- - + -------|*3 / - -- + -------------------------- - a || | | 3*|- - + -------|*3 / - -- + -------------------------- - a ||
\ \ \/ 2 2 // \ \ \/ 2 2 // \ \ \ 2 2 / \/ 2 2 // \ \ \ 2 2 / \/ 2 2 // \ \ \ 2 2 / \/ 2 2 // \ \ \ 2 2 / \/ 2 2 // \ \ \/ 2 2 // \ \ \/ 2 2 // \ \ \ 2 2 / \/ 2 2 // \ \ \ 2 2 / \/ 2 2 // \ \ \ 2 2 / \/ 2 2 // \ \ \ 2 2 / \/ 2 2 //
$$\left(\left(\left(\left(\left(- \operatorname{re}{\left(\operatorname{acos}{\left(- \frac{a^{2}}{3 \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}} - \frac{2 a}{3} - \frac{\sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}}{3} \right)}\right)} - i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{a^{2}}{3 \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}} - \frac{2 a}{3} - \frac{\sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}}{3} \right)}\right)} + 2 \pi\right) + \left(- \operatorname{re}{\left(\operatorname{acos}{\left(- \frac{a^{2}}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}} - \frac{2 a}{3} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}}{3} \right)}\right)} - i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{a^{2}}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}} - \frac{2 a}{3} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}}{3} \right)}\right)} + 2 \pi\right)\right) + \left(- \operatorname{re}{\left(\operatorname{acos}{\left(- \frac{a^{2}}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}} - \frac{2 a}{3} - \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}}{3} \right)}\right)} - i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{a^{2}}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}} - \frac{2 a}{3} - \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}}{3} \right)}\right)} + 2 \pi\right)\right) + \left(\operatorname{re}{\left(\operatorname{acos}{\left(- \frac{a^{2}}{3 \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}} - \frac{2 a}{3} - \frac{\sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{a^{2}}{3 \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}} - \frac{2 a}{3} - \frac{\sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}}{3} \right)}\right)}\right)\right) + \left(\operatorname{re}{\left(\operatorname{acos}{\left(- \frac{a^{2}}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}} - \frac{2 a}{3} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{a^{2}}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}} - \frac{2 a}{3} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}}{3} \right)}\right)}\right)\right) + \left(\operatorname{re}{\left(\operatorname{acos}{\left(- \frac{a^{2}}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}} - \frac{2 a}{3} - \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{a^{2}}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}} - \frac{2 a}{3} - \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}}{3} \right)}\right)}\right)$$
=
6*pi
$$6 \pi$$
producto
/ / / ________________________________________ \\ / / ________________________________________ \\\ / / / ________________________________________ \\ / / ________________________________________ \\\ / / / ________________________________________ \\ / / ________________________________________ \\\ / / / ________________________________________ \\ / / ________________________________________ \\\ / / / ________________________________________ \\ / / ________________________________________ \\\ / / / ________________________________________ \\ / / ________________________________________ \\\ | | | / ______________________ || | | / ______________________ ||| | | | / ______________________ || | | / ______________________ ||| | | | / ______________________ || | | / ______________________ ||| | | | / ______________________ || | | / ______________________ ||| | | | / ______________________ || | | / ______________________ ||| | | | / ______________________ || | | / ______________________ ||| | | | / / 2 || | | / / 2 ||| | | | / / 2 || | | / / 2 ||| | | | / / 2 || | | / / 2 ||| | | | / / 2 || | | / / 2 ||| | | | / / 2 || | | / / 2 ||| | | | / / 2 || | | / / 2 ||| | | | / / / 3\ 6 || | | / / / 3\ 6 ||| | | | / / / 3\ 6 / ___\ || | | / / / 3\ 6 / ___\ ||| | | | / / / 3\ 6 / ___\ || | | / / / 3\ 6 / ___\ ||| | | | / / / 3\ 6 || | | / / / 3\ 6 ||| | | | / / / 3\ 6 / ___\ || | | / / / 3\ 6 / ___\ ||| | | | / / / 3\ 6 / ___\ || | | / / / 3\ 6 / ___\ ||| | | | / 27 \/ \-27 - 2*a / - 4*a 3 || | | / 27 \/ \-27 - 2*a / - 4*a 3 ||| | | | / 27 \/ \-27 - 2*a / - 4*a 3 | 1 I*\/ 3 | || | | / 27 \/ \-27 - 2*a / - 4*a 3 | 1 I*\/ 3 | ||| | | | / 27 \/ \-27 - 2*a / - 4*a 3 | 1 I*\/ 3 | || | | / 27 \/ \-27 - 2*a / - 4*a 3 | 1 I*\/ 3 | ||| | | | / 27 \/ \-27 - 2*a / - 4*a 3 || | | / 27 \/ \-27 - 2*a / - 4*a 3 ||| | | | / 27 \/ \-27 - 2*a / - 4*a 3 | 1 I*\/ 3 | || | | / 27 \/ \-27 - 2*a / - 4*a 3 | 1 I*\/ 3 | ||| | | | / 27 \/ \-27 - 2*a / - 4*a 3 | 1 I*\/ 3 | || | | / 27 \/ \-27 - 2*a / - 4*a 3 | 1 I*\/ 3 | ||| | | | 3 / - -- + -------------------------- - a 2 || | | 3 / - -- + -------------------------- - a 2 ||| | | | 3 / - -- + -------------------------- - a *|- - - -------| 2 || | | 3 / - -- + -------------------------- - a *|- - - -------| 2 ||| | | | 3 / - -- + -------------------------- - a *|- - + -------| 2 || | | 3 / - -- + -------------------------- - a *|- - + -------| 2 ||| | | | 3 / - -- + -------------------------- - a 2 || | | 3 / - -- + -------------------------- - a 2 ||| | | | 3 / - -- + -------------------------- - a *|- - - -------| 2 || | | 3 / - -- + -------------------------- - a *|- - - -------| 2 ||| | | | 3 / - -- + -------------------------- - a *|- - + -------| 2 || | | 3 / - -- + -------------------------- - a *|- - + -------| 2 ||| | | | 2*a \/ 2 2 a || | | 2*a \/ 2 2 a ||| | | | 2*a \/ 2 2 \ 2 2 / a || | | 2*a \/ 2 2 \ 2 2 / a ||| | | | 2*a \/ 2 2 \ 2 2 / a || | | 2*a \/ 2 2 \ 2 2 / a ||| | | | 2*a \/ 2 2 a || | | 2*a \/ 2 2 a ||| | | | 2*a \/ 2 2 \ 2 2 / a || | | 2*a \/ 2 2 \ 2 2 / a ||| | | | 2*a \/ 2 2 \ 2 2 / a || | | 2*a \/ 2 2 \ 2 2 / a ||| |- re|acos|- --- - ----------------------------------------------- - -------------------------------------------------|| + 2*pi - I*im|acos|- --- - ----------------------------------------------- - -------------------------------------------------|||*|- re|acos|- --- - --------------------------------------------------------------- - -----------------------------------------------------------------|| + 2*pi - I*im|acos|- --- - --------------------------------------------------------------- - -----------------------------------------------------------------|||*|- re|acos|- --- - --------------------------------------------------------------- - -----------------------------------------------------------------|| + 2*pi - I*im|acos|- --- - --------------------------------------------------------------- - -----------------------------------------------------------------|||*|I*im|acos|- --- - ----------------------------------------------- - -------------------------------------------------|| + re|acos|- --- - ----------------------------------------------- - -------------------------------------------------|||*|I*im|acos|- --- - --------------------------------------------------------------- - -----------------------------------------------------------------|| + re|acos|- --- - --------------------------------------------------------------- - -----------------------------------------------------------------|||*|I*im|acos|- --- - --------------------------------------------------------------- - -----------------------------------------------------------------|| + re|acos|- --- - --------------------------------------------------------------- - -----------------------------------------------------------------||| | | | 3 3 ________________________________________|| | | 3 3 ________________________________________||| | | | 3 3 ________________________________________|| | | 3 3 ________________________________________||| | | | 3 3 ________________________________________|| | | 3 3 ________________________________________||| | | | 3 3 ________________________________________|| | | 3 3 ________________________________________||| | | | 3 3 ________________________________________|| | | 3 3 ________________________________________||| | | | 3 3 ________________________________________|| | | 3 3 ________________________________________||| | | | / ______________________ || | | / ______________________ ||| | | | / ______________________ || | | / ______________________ ||| | | | / ______________________ || | | / ______________________ ||| | | | / ______________________ || | | / ______________________ ||| | | | / ______________________ || | | / ______________________ ||| | | | / ______________________ || | | / ______________________ ||| | | | / / 2 || | | / / 2 ||| | | | / / 2 || | | / / 2 ||| | | | / / 2 || | | / / 2 ||| | | | / / 2 || | | / / 2 ||| | | | / / 2 || | | / / 2 ||| | | | / / 2 || | | / / 2 ||| | | | / / / 3\ 6 || | | / / / 3\ 6 ||| | | | / ___\ / / / 3\ 6 || | | / ___\ / / / 3\ 6 ||| | | | / ___\ / / / 3\ 6 || | | / ___\ / / / 3\ 6 ||| | | | / / / 3\ 6 || | | / / / 3\ 6 ||| | | | / ___\ / / / 3\ 6 || | | / ___\ / / / 3\ 6 ||| | | | / ___\ / / / 3\ 6 || | | / ___\ / / / 3\ 6 ||| | | | / 27 \/ \-27 - 2*a / - 4*a 3 || | | / 27 \/ \-27 - 2*a / - 4*a 3 ||| | | | | 1 I*\/ 3 | / 27 \/ \-27 - 2*a / - 4*a 3 || | | | 1 I*\/ 3 | / 27 \/ \-27 - 2*a / - 4*a 3 ||| | | | | 1 I*\/ 3 | / 27 \/ \-27 - 2*a / - 4*a 3 || | | | 1 I*\/ 3 | / 27 \/ \-27 - 2*a / - 4*a 3 ||| | | | / 27 \/ \-27 - 2*a / - 4*a 3 || | | / 27 \/ \-27 - 2*a / - 4*a 3 ||| | | | | 1 I*\/ 3 | / 27 \/ \-27 - 2*a / - 4*a 3 || | | | 1 I*\/ 3 | / 27 \/ \-27 - 2*a / - 4*a 3 ||| | | | | 1 I*\/ 3 | / 27 \/ \-27 - 2*a / - 4*a 3 || | | | 1 I*\/ 3 | / 27 \/ \-27 - 2*a / - 4*a 3 ||| | | | 3*3 / - -- + -------------------------- - a || | | 3*3 / - -- + -------------------------- - a ||| | | | 3*|- - - -------|*3 / - -- + -------------------------- - a || | | 3*|- - - -------|*3 / - -- + -------------------------- - a ||| | | | 3*|- - + -------|*3 / - -- + -------------------------- - a || | | 3*|- - + -------|*3 / - -- + -------------------------- - a ||| | | | 3*3 / - -- + -------------------------- - a || | | 3*3 / - -- + -------------------------- - a ||| | | | 3*|- - - -------|*3 / - -- + -------------------------- - a || | | 3*|- - - -------|*3 / - -- + -------------------------- - a ||| | | | 3*|- - + -------|*3 / - -- + -------------------------- - a || | | 3*|- - + -------|*3 / - -- + -------------------------- - a ||| \ \ \ \/ 2 2 // \ \ \/ 2 2 /// \ \ \ \ 2 2 / \/ 2 2 // \ \ \ 2 2 / \/ 2 2 /// \ \ \ \ 2 2 / \/ 2 2 // \ \ \ 2 2 / \/ 2 2 /// \ \ \ \/ 2 2 // \ \ \/ 2 2 /// \ \ \ \ 2 2 / \/ 2 2 // \ \ \ 2 2 / \/ 2 2 /// \ \ \ \ 2 2 / \/ 2 2 // \ \ \ 2 2 / \/ 2 2 ///
$$\left(- \operatorname{re}{\left(\operatorname{acos}{\left(- \frac{a^{2}}{3 \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}} - \frac{2 a}{3} - \frac{\sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}}{3} \right)}\right)} - i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{a^{2}}{3 \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}} - \frac{2 a}{3} - \frac{\sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}}{3} \right)}\right)} + 2 \pi\right) \left(- \operatorname{re}{\left(\operatorname{acos}{\left(- \frac{a^{2}}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}} - \frac{2 a}{3} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}}{3} \right)}\right)} - i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{a^{2}}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}} - \frac{2 a}{3} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}}{3} \right)}\right)} + 2 \pi\right) \left(- \operatorname{re}{\left(\operatorname{acos}{\left(- \frac{a^{2}}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}} - \frac{2 a}{3} - \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}}{3} \right)}\right)} - i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{a^{2}}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}} - \frac{2 a}{3} - \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}}{3} \right)}\right)} + 2 \pi\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(- \frac{a^{2}}{3 \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}} - \frac{2 a}{3} - \frac{\sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{a^{2}}{3 \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}} - \frac{2 a}{3} - \frac{\sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}}{3} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(- \frac{a^{2}}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}} - \frac{2 a}{3} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{a^{2}}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}} - \frac{2 a}{3} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}}{3} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(- \frac{a^{2}}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}} - \frac{2 a}{3} - \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{a^{2}}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}} - \frac{2 a}{3} - \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- a^{3} + \frac{\sqrt{- 4 a^{6} + \left(- 2 a^{3} - 27\right)^{2}}}{2} - \frac{27}{2}}}{3} \right)}\right)}\right)$$
=
/ / / ________________________________________ / ________________________________________ \\\ / / ________________________________________ / ________________________________________ \\\\ / / / ________________________________________ / ________________________________________ \\\ / / ________________________________________ / ________________________________________ \\\\ / / / ________________________________________ / ________________________________________ \\\ / / ________________________________________ / ________________________________________ \\\\ / / / ________________________________________ / ________________________________________ \\\ / / ________________________________________ / ________________________________________ \\\\
/ / / / 2/3 _____________________________________\ \\ / / / 2/3 _____________________________________\ \\\ | | | / _____________________ | / _____________________ ||| | | / _____________________ | / _____________________ |||| | | | / _____________________ | / _____________________ ||| | | / _____________________ | / _____________________ |||| / / / / 2/3 _____________________________________\ \\ / / / 2/3 _____________________________________\ \\\ | | | / _____________________ | / _____________________ ||| | | / _____________________ | / _____________________ |||| | | | / _____________________ | / _____________________ ||| | | / _____________________ | / _____________________ ||||
| | | | / ___________\ / ___________ | || | | | / ___________\ / ___________ | ||| | | | / / 2 | / / 2 ||| | | / / 2 | / / 2 |||| | | | / / 2 | / / 2 ||| | | / / 2 | / / 2 |||| | | | | / ___________\ / ___________ | || | | | / ___________\ / ___________ | ||| | | | / / 2 | / / 2 ||| | | / / 2 | / / 2 |||| | | | / / 2 | / / 2 ||| | | / / 2 | / / 2 ||||
| | | | 2/3 | 3 ___ / 3 | 3 ___ 2 3 / 3 ___ / 3 | || | | | 2/3 | 3 ___ / 3 | 3 ___ 2 3 / 3 ___ / 3 | ||| | | | 3 ___ 2 3 / / / 3\ 6 3 / ___\ | 2/3 3 / / / 3\ 6 3 / ___\||| | | 3 ___ 2 3 / / / 3\ 6 3 / ___\ | 2/3 3 / / / 3\ 6 3 / ___\|||| | | | 3 ___ 2 3 / / / 3\ 6 3 / ___\ | 2/3 3 / / / 3\ 6 3 / ___\||| | | 3 ___ 2 3 / / / 3\ 6 3 / ___\ | 2/3 3 / / / 3\ 6 3 / ___\|||| | | | | 2/3 | 3 ___ / 3 | 3 ___ 2 3 / 3 ___ / 3 | || | | | 2/3 | 3 ___ / 3 | 3 ___ 2 3 / 3 ___ / 3 | ||| | | | 3 ___ 2 3 / / / 3\ 6 3 / ___\ | 2/3 3 / / / 3\ 6 3 / ___\||| | | 3 ___ 2 3 / / / 3\ 6 3 / ___\ | 2/3 3 / / / 3\ 6 3 / ___\|||| | | | 3 ___ 2 3 / / / 3\ 6 3 / ___\ | 2/3 3 / / / 3\ 6 3 / ___\||| | | 3 ___ 2 3 / / / 3\ 6 3 / ___\ | 2/3 3 / / / 3\ 6 3 / ___\||||
| | |-\2 *\-27 - 2*a + 3*\/ 3 *\/ 27 + 4*a / + 2*\/ 2 *a + 4*a*\/ -27 - 2*a + 3*\/ 3 *\/ 27 + 4*a / || | |-\2 *\-27 - 2*a + 3*\/ 3 *\/ 27 + 4*a / + 2*\/ 2 *a + 4*a*\/ -27 - 2*a + 3*\/ 3 *\/ 27 + 4*a / ||| | | |8*\/ 2 *a - \/ -27 + \/ \27 + 2*a / - 4*a - 2*a *\1 + I*\/ 3 /*\8*a - 2 *\/ -27 + \/ \27 + 2*a / - 4*a - 2*a *\1 + I*\/ 3 //|| | |8*\/ 2 *a - \/ -27 + \/ \27 + 2*a / - 4*a - 2*a *\1 + I*\/ 3 /*\8*a - 2 *\/ -27 + \/ \27 + 2*a / - 4*a - 2*a *\1 + I*\/ 3 //||| | | |8*\/ 2 *a - \/ -27 + \/ \27 + 2*a / - 4*a - 2*a *\1 - I*\/ 3 /*\8*a - 2 *\/ -27 + \/ \27 + 2*a / - 4*a - 2*a *\1 - I*\/ 3 //|| | |8*\/ 2 *a - \/ -27 + \/ \27 + 2*a / - 4*a - 2*a *\1 - I*\/ 3 /*\8*a - 2 *\/ -27 + \/ \27 + 2*a / - 4*a - 2*a *\1 - I*\/ 3 //||| | | |-\2 *\-27 - 2*a + 3*\/ 3 *\/ 27 + 4*a / + 2*\/ 2 *a + 4*a*\/ -27 - 2*a + 3*\/ 3 *\/ 27 + 4*a / || | |-\2 *\-27 - 2*a + 3*\/ 3 *\/ 27 + 4*a / + 2*\/ 2 *a + 4*a*\/ -27 - 2*a + 3*\/ 3 *\/ 27 + 4*a / ||| | | |8*\/ 2 *a - \/ -27 + \/ \27 + 2*a / - 4*a - 2*a *\1 + I*\/ 3 /*\8*a - 2 *\/ -27 + \/ \27 + 2*a / - 4*a - 2*a *\1 + I*\/ 3 //|| | |8*\/ 2 *a - \/ -27 + \/ \27 + 2*a / - 4*a - 2*a *\1 + I*\/ 3 /*\8*a - 2 *\/ -27 + \/ \27 + 2*a / - 4*a - 2*a *\1 + I*\/ 3 //||| | | |8*\/ 2 *a - \/ -27 + \/ \27 + 2*a / - 4*a - 2*a *\1 - I*\/ 3 /*\8*a - 2 *\/ -27 + \/ \27 + 2*a / - 4*a - 2*a *\1 - I*\/ 3 //|| | |8*\/ 2 *a - \/ -27 + \/ \27 + 2*a / - 4*a - 2*a *\1 - I*\/ 3 /*\8*a - 2 *\/ -27 + \/ \27 + 2*a / - 4*a - 2*a *\1 - I*\/ 3 //|||
-|I*im|acos|--------------------------------------------------------------------------------------------------------------|| + re|acos|--------------------------------------------------------------------------------------------------------------|||*|I*im|acos|-------------------------------------------------------------------------------------------------------------------------------------------------|| + re|acos|-------------------------------------------------------------------------------------------------------------------------------------------------|||*|I*im|acos|-------------------------------------------------------------------------------------------------------------------------------------------------|| + re|acos|-------------------------------------------------------------------------------------------------------------------------------------------------|||*|-2*pi + I*im|acos|--------------------------------------------------------------------------------------------------------------|| + re|acos|--------------------------------------------------------------------------------------------------------------|||*|-2*pi + I*im|acos|-------------------------------------------------------------------------------------------------------------------------------------------------|| + re|acos|-------------------------------------------------------------------------------------------------------------------------------------------------|||*|-2*pi + I*im|acos|-------------------------------------------------------------------------------------------------------------------------------------------------|| + re|acos|-------------------------------------------------------------------------------------------------------------------------------------------------|||
| | | _____________________________________ || | | _____________________________________ ||| | | | ________________________________________ || | | ________________________________________ ||| | | | ________________________________________ || | | ________________________________________ ||| | | | _____________________________________ || | | _____________________________________ ||| | | | ________________________________________ || | | ________________________________________ ||| | | | ________________________________________ || | | ________________________________________ |||
| | | / ___________ || | | / ___________ ||| | | | / _____________________ || | | / _____________________ ||| | | | / _____________________ || | | / _____________________ ||| | | | / ___________ || | | / ___________ ||| | | | / _____________________ || | | / _____________________ ||| | | | / _____________________ || | | / _____________________ |||
| | | 3 / 3 ___ / 3 || | | 3 / 3 ___ / 3 ||| | | | / / 2 || | | / / 2 ||| | | | / / 2 || | | / / 2 ||| | | | 3 / 3 ___ / 3 || | | 3 / 3 ___ / 3 ||| | | | / / 2 || | | / / 2 ||| | | | / / 2 || | | / / 2 |||
\ \ \ 6*\/ -27 - 2*a + 3*\/ 3 *\/ 27 + 4*a // \ \ 6*\/ -27 - 2*a + 3*\/ 3 *\/ 27 + 4*a /// | | | / ___\ 3 / / / 3\ 6 3 || | | / ___\ 3 / / / 3\ 6 3 ||| | | | / ___\ 3 / / / 3\ 6 3 || | | / ___\ 3 / / / 3\ 6 3 ||| \ \ \ 6*\/ -27 - 2*a + 3*\/ 3 *\/ 27 + 4*a // \ \ 6*\/ -27 - 2*a + 3*\/ 3 *\/ 27 + 4*a /// | | | / ___\ 3 / / / 3\ 6 3 || | | / ___\ 3 / / / 3\ 6 3 ||| | | | / ___\ 3 / / / 3\ 6 3 || | | / ___\ 3 / / / 3\ 6 3 |||
\ \ \ 12*\1 + I*\/ 3 /*\/ -27 + \/ \27 + 2*a / - 4*a - 2*a // \ \ 12*\1 + I*\/ 3 /*\/ -27 + \/ \27 + 2*a / - 4*a - 2*a /// \ \ \ 12*\1 - I*\/ 3 /*\/ -27 + \/ \27 + 2*a / - 4*a - 2*a // \ \ 12*\1 - I*\/ 3 /*\/ -27 + \/ \27 + 2*a / - 4*a - 2*a /// \ \ \ 12*\1 + I*\/ 3 /*\/ -27 + \/ \27 + 2*a / - 4*a - 2*a // \ \ 12*\1 + I*\/ 3 /*\/ -27 + \/ \27 + 2*a / - 4*a - 2*a /// \ \ \ 12*\1 - I*\/ 3 /*\/ -27 + \/ \27 + 2*a / - 4*a - 2*a // \ \ 12*\1 - I*\/ 3 /*\/ -27 + \/ \27 + 2*a / - 4*a - 2*a ///
$$- \left(\operatorname{re}{\left(\operatorname{acos}{\left(- \frac{2 \sqrt[3]{2} a^{2} + 4 a \sqrt[3]{- 2 a^{3} + 3 \sqrt{3} \sqrt{4 a^{3} + 27} - 27} + 2^{\frac{2}{3}} \left(- 2 a^{3} + 3 \sqrt{3} \sqrt{4 a^{3} + 27} - 27\right)^{\frac{2}{3}}}{6 \sqrt[3]{- 2 a^{3} + 3 \sqrt{3} \sqrt{4 a^{3} + 27} - 27}} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{2 \sqrt[3]{2} a^{2} + 4 a \sqrt[3]{- 2 a^{3} + 3 \sqrt{3} \sqrt{4 a^{3} + 27} - 27} + 2^{\frac{2}{3}} \left(- 2 a^{3} + 3 \sqrt{3} \sqrt{4 a^{3} + 27} - 27\right)^{\frac{2}{3}}}{6 \sqrt[3]{- 2 a^{3} + 3 \sqrt{3} \sqrt{4 a^{3} + 27} - 27}} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(\frac{8 \sqrt[3]{2} a^{2} - \left(1 - \sqrt{3} i\right) \left(8 a - 2^{\frac{2}{3}} \left(1 - \sqrt{3} i\right) \sqrt[3]{- 2 a^{3} + \sqrt{- 4 a^{6} + \left(2 a^{3} + 27\right)^{2}} - 27}\right) \sqrt[3]{- 2 a^{3} + \sqrt{- 4 a^{6} + \left(2 a^{3} + 27\right)^{2}} - 27}}{12 \left(1 - \sqrt{3} i\right) \sqrt[3]{- 2 a^{3} + \sqrt{- 4 a^{6} + \left(2 a^{3} + 27\right)^{2}} - 27}} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{8 \sqrt[3]{2} a^{2} - \left(1 - \sqrt{3} i\right) \left(8 a - 2^{\frac{2}{3}} \left(1 - \sqrt{3} i\right) \sqrt[3]{- 2 a^{3} + \sqrt{- 4 a^{6} + \left(2 a^{3} + 27\right)^{2}} - 27}\right) \sqrt[3]{- 2 a^{3} + \sqrt{- 4 a^{6} + \left(2 a^{3} + 27\right)^{2}} - 27}}{12 \left(1 - \sqrt{3} i\right) \sqrt[3]{- 2 a^{3} + \sqrt{- 4 a^{6} + \left(2 a^{3} + 27\right)^{2}} - 27}} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(\frac{8 \sqrt[3]{2} a^{2} - \left(1 + \sqrt{3} i\right) \left(8 a - 2^{\frac{2}{3}} \left(1 + \sqrt{3} i\right) \sqrt[3]{- 2 a^{3} + \sqrt{- 4 a^{6} + \left(2 a^{3} + 27\right)^{2}} - 27}\right) \sqrt[3]{- 2 a^{3} + \sqrt{- 4 a^{6} + \left(2 a^{3} + 27\right)^{2}} - 27}}{12 \left(1 + \sqrt{3} i\right) \sqrt[3]{- 2 a^{3} + \sqrt{- 4 a^{6} + \left(2 a^{3} + 27\right)^{2}} - 27}} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{8 \sqrt[3]{2} a^{2} - \left(1 + \sqrt{3} i\right) \left(8 a - 2^{\frac{2}{3}} \left(1 + \sqrt{3} i\right) \sqrt[3]{- 2 a^{3} + \sqrt{- 4 a^{6} + \left(2 a^{3} + 27\right)^{2}} - 27}\right) \sqrt[3]{- 2 a^{3} + \sqrt{- 4 a^{6} + \left(2 a^{3} + 27\right)^{2}} - 27}}{12 \left(1 + \sqrt{3} i\right) \sqrt[3]{- 2 a^{3} + \sqrt{- 4 a^{6} + \left(2 a^{3} + 27\right)^{2}} - 27}} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(- \frac{2 \sqrt[3]{2} a^{2} + 4 a \sqrt[3]{- 2 a^{3} + 3 \sqrt{3} \sqrt{4 a^{3} + 27} - 27} + 2^{\frac{2}{3}} \left(- 2 a^{3} + 3 \sqrt{3} \sqrt{4 a^{3} + 27} - 27\right)^{\frac{2}{3}}}{6 \sqrt[3]{- 2 a^{3} + 3 \sqrt{3} \sqrt{4 a^{3} + 27} - 27}} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{2 \sqrt[3]{2} a^{2} + 4 a \sqrt[3]{- 2 a^{3} + 3 \sqrt{3} \sqrt{4 a^{3} + 27} - 27} + 2^{\frac{2}{3}} \left(- 2 a^{3} + 3 \sqrt{3} \sqrt{4 a^{3} + 27} - 27\right)^{\frac{2}{3}}}{6 \sqrt[3]{- 2 a^{3} + 3 \sqrt{3} \sqrt{4 a^{3} + 27} - 27}} \right)}\right)} - 2 \pi\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(\frac{8 \sqrt[3]{2} a^{2} - \left(1 - \sqrt{3} i\right) \left(8 a - 2^{\frac{2}{3}} \left(1 - \sqrt{3} i\right) \sqrt[3]{- 2 a^{3} + \sqrt{- 4 a^{6} + \left(2 a^{3} + 27\right)^{2}} - 27}\right) \sqrt[3]{- 2 a^{3} + \sqrt{- 4 a^{6} + \left(2 a^{3} + 27\right)^{2}} - 27}}{12 \left(1 - \sqrt{3} i\right) \sqrt[3]{- 2 a^{3} + \sqrt{- 4 a^{6} + \left(2 a^{3} + 27\right)^{2}} - 27}} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{8 \sqrt[3]{2} a^{2} - \left(1 - \sqrt{3} i\right) \left(8 a - 2^{\frac{2}{3}} \left(1 - \sqrt{3} i\right) \sqrt[3]{- 2 a^{3} + \sqrt{- 4 a^{6} + \left(2 a^{3} + 27\right)^{2}} - 27}\right) \sqrt[3]{- 2 a^{3} + \sqrt{- 4 a^{6} + \left(2 a^{3} + 27\right)^{2}} - 27}}{12 \left(1 - \sqrt{3} i\right) \sqrt[3]{- 2 a^{3} + \sqrt{- 4 a^{6} + \left(2 a^{3} + 27\right)^{2}} - 27}} \right)}\right)} - 2 \pi\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(\frac{8 \sqrt[3]{2} a^{2} - \left(1 + \sqrt{3} i\right) \left(8 a - 2^{\frac{2}{3}} \left(1 + \sqrt{3} i\right) \sqrt[3]{- 2 a^{3} + \sqrt{- 4 a^{6} + \left(2 a^{3} + 27\right)^{2}} - 27}\right) \sqrt[3]{- 2 a^{3} + \sqrt{- 4 a^{6} + \left(2 a^{3} + 27\right)^{2}} - 27}}{12 \left(1 + \sqrt{3} i\right) \sqrt[3]{- 2 a^{3} + \sqrt{- 4 a^{6} + \left(2 a^{3} + 27\right)^{2}} - 27}} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{8 \sqrt[3]{2} a^{2} - \left(1 + \sqrt{3} i\right) \left(8 a - 2^{\frac{2}{3}} \left(1 + \sqrt{3} i\right) \sqrt[3]{- 2 a^{3} + \sqrt{- 4 a^{6} + \left(2 a^{3} + 27\right)^{2}} - 27}\right) \sqrt[3]{- 2 a^{3} + \sqrt{- 4 a^{6} + \left(2 a^{3} + 27\right)^{2}} - 27}}{12 \left(1 + \sqrt{3} i\right) \sqrt[3]{- 2 a^{3} + \sqrt{- 4 a^{6} + \left(2 a^{3} + 27\right)^{2}} - 27}} \right)}\right)} - 2 \pi\right)$$
-(i*im(acos(-(2^(2/3)*(-27 - 2*a^3 + 3*sqrt(3)*sqrt(27 + 4*a^3))^(2/3) + 2*2^(1/3)*a^2 + 4*a*(-27 - 2*a^3 + 3*sqrt(3)*sqrt(27 + 4*a^3))^(1/3))/(6*(-27 - 2*a^3 + 3*sqrt(3)*sqrt(27 + 4*a^3))^(1/3)))) + re(acos(-(2^(2/3)*(-27 - 2*a^3 + 3*sqrt(3)*sqrt(27 + 4*a^3))^(2/3) + 2*2^(1/3)*a^2 + 4*a*(-27 - 2*a^3 + 3*sqrt(3)*sqrt(27 + 4*a^3))^(1/3))/(6*(-27 - 2*a^3 + 3*sqrt(3)*sqrt(27 + 4*a^3))^(1/3)))))*(i*im(acos((8*2^(1/3)*a^2 - (-27 + sqrt((27 + 2*a^3)^2 - 4*a^6) - 2*a^3)^(1/3)*(1 + i*sqrt(3))*(8*a - 2^(2/3)*(-27 + sqrt((27 + 2*a^3)^2 - 4*a^6) - 2*a^3)^(1/3)*(1 + i*sqrt(3))))/(12*(1 + i*sqrt(3))*(-27 + sqrt((27 + 2*a^3)^2 - 4*a^6) - 2*a^3)^(1/3)))) + re(acos((8*2^(1/3)*a^2 - (-27 + sqrt((27 + 2*a^3)^2 - 4*a^6) - 2*a^3)^(1/3)*(1 + i*sqrt(3))*(8*a - 2^(2/3)*(-27 + sqrt((27 + 2*a^3)^2 - 4*a^6) - 2*a^3)^(1/3)*(1 + i*sqrt(3))))/(12*(1 + i*sqrt(3))*(-27 + sqrt((27 + 2*a^3)^2 - 4*a^6) - 2*a^3)^(1/3)))))*(i*im(acos((8*2^(1/3)*a^2 - (-27 + sqrt((27 + 2*a^3)^2 - 4*a^6) - 2*a^3)^(1/3)*(1 - i*sqrt(3))*(8*a - 2^(2/3)*(-27 + sqrt((27 + 2*a^3)^2 - 4*a^6) - 2*a^3)^(1/3)*(1 - i*sqrt(3))))/(12*(1 - i*sqrt(3))*(-27 + sqrt((27 + 2*a^3)^2 - 4*a^6) - 2*a^3)^(1/3)))) + re(acos((8*2^(1/3)*a^2 - (-27 + sqrt((27 + 2*a^3)^2 - 4*a^6) - 2*a^3)^(1/3)*(1 - i*sqrt(3))*(8*a - 2^(2/3)*(-27 + sqrt((27 + 2*a^3)^2 - 4*a^6) - 2*a^3)^(1/3)*(1 - i*sqrt(3))))/(12*(1 - i*sqrt(3))*(-27 + sqrt((27 + 2*a^3)^2 - 4*a^6) - 2*a^3)^(1/3)))))*(-2*pi + i*im(acos(-(2^(2/3)*(-27 - 2*a^3 + 3*sqrt(3)*sqrt(27 + 4*a^3))^(2/3) + 2*2^(1/3)*a^2 + 4*a*(-27 - 2*a^3 + 3*sqrt(3)*sqrt(27 + 4*a^3))^(1/3))/(6*(-27 - 2*a^3 + 3*sqrt(3)*sqrt(27 + 4*a^3))^(1/3)))) + re(acos(-(2^(2/3)*(-27 - 2*a^3 + 3*sqrt(3)*sqrt(27 + 4*a^3))^(2/3) + 2*2^(1/3)*a^2 + 4*a*(-27 - 2*a^3 + 3*sqrt(3)*sqrt(27 + 4*a^3))^(1/3))/(6*(-27 - 2*a^3 + 3*sqrt(3)*sqrt(27 + 4*a^3))^(1/3)))))*(-2*pi + i*im(acos((8*2^(1/3)*a^2 - (-27 + sqrt((27 + 2*a^3)^2 - 4*a^6) - 2*a^3)^(1/3)*(1 + i*sqrt(3))*(8*a - 2^(2/3)*(-27 + sqrt((27 + 2*a^3)^2 - 4*a^6) - 2*a^3)^(1/3)*(1 + i*sqrt(3))))/(12*(1 + i*sqrt(3))*(-27 + sqrt((27 + 2*a^3)^2 - 4*a^6) - 2*a^3)^(1/3)))) + re(acos((8*2^(1/3)*a^2 - (-27 + sqrt((27 + 2*a^3)^2 - 4*a^6) - 2*a^3)^(1/3)*(1 + i*sqrt(3))*(8*a - 2^(2/3)*(-27 + sqrt((27 + 2*a^3)^2 - 4*a^6) - 2*a^3)^(1/3)*(1 + i*sqrt(3))))/(12*(1 + i*sqrt(3))*(-27 + sqrt((27 + 2*a^3)^2 - 4*a^6) - 2*a^3)^(1/3)))))*(-2*pi + i*im(acos((8*2^(1/3)*a^2 - (-27 + sqrt((27 + 2*a^3)^2 - 4*a^6) - 2*a^3)^(1/3)*(1 - i*sqrt(3))*(8*a - 2^(2/3)*(-27 + sqrt((27 + 2*a^3)^2 - 4*a^6) - 2*a^3)^(1/3)*(1 - i*sqrt(3))))/(12*(1 - i*sqrt(3))*(-27 + sqrt((27 + 2*a^3)^2 - 4*a^6) - 2*a^3)^(1/3)))) + re(acos((8*2^(1/3)*a^2 - (-27 + sqrt((27 + 2*a^3)^2 - 4*a^6) - 2*a^3)^(1/3)*(1 - i*sqrt(3))*(8*a - 2^(2/3)*(-27 + sqrt((27 + 2*a^3)^2 - 4*a^6) - 2*a^3)^(1/3)*(1 - i*sqrt(3))))/(12*(1 - i*sqrt(3))*(-27 + sqrt((27 + 2*a^3)^2 - 4*a^6) - 2*a^3)^(1/3)))))