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sqrt(30)*log(x-10*sqrt(30))/2-sqrt(30)*log(x+10*sqrt(30))/2=Const-t la ecuación

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Solución

Ha introducido [src]
  ____    /         ____\     ____    /         ____\        
\/ 30 *log\x - 10*\/ 30 /   \/ 30 *log\x + 10*\/ 30 /        
------------------------- - ------------------------- = c - t
            2                           2                    
$$\frac{\sqrt{30} \log{\left(x - 10 \sqrt{30} \right)}}{2} - \frac{\sqrt{30} \log{\left(x + 10 \sqrt{30} \right)}}{2} = c - t$$
Gráfica
Respuesta rápida [src]
                                                                                                  /    ____           ____      \     /    ____           ____      \                                                                                                                                                                             /    ____           ____      \    /    ____           ____      \                                                                              
                                                                                         ____     |  \/ 30 *re(t)   \/ 30 *re(c)|     |  \/ 30 *re(t)   \/ 30 *re(c)|                                                                                                                                                                     ____    |  \/ 30 *im(t)   \/ 30 *im(c)|    |  \/ 30 *im(t)   \/ 30 *im(c)|                                                                              
                                                                                    10*\/ 30 *cosh|- ------------ + ------------|*sinh|- ------------ + ------------|                                                                                                                                                              10*I*\/ 30 *cos|- ------------ + ------------|*sin|- ------------ + ------------|                                                                              
                                                                                                  \       30             30     /     \       30             30     /                                                                                                                                                                             \       30             30     /    \       30             30     /                                                                              
x1 = - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                    /       /    ____           ____      \     /    ____           ____      \             /    ____           ____      \      /    ____           ____      \  \                                                                                /       /    ____           ____      \     /    ____           ____      \             /    ____           ____      \      /    ____           ____      \  \
                                                                                    |      2|  \/ 30 *im(t)   \/ 30 *im(c)|    2|  \/ 30 *im(t)   \/ 30 *im(c)|            2|  \/ 30 *re(t)   \/ 30 *re(c)|     2|  \/ 30 *re(t)   \/ 30 *re(c)|  |                                                                                |      2|  \/ 30 *im(t)   \/ 30 *im(c)|    2|  \/ 30 *im(t)   \/ 30 *im(c)|            2|  \/ 30 *re(t)   \/ 30 *re(c)|     2|  \/ 30 *re(t)   \/ 30 *re(c)|  |
       /    /    ____           ____      \        /    ____           ____      \\ |   cos |- ------------ + ------------|*sin |- ------------ + ------------|        cosh |- ------------ + ------------|*sinh |- ------------ + ------------|  |   /    /    ____           ____      \        /    ____           ____      \\ |   cos |- ------------ + ------------|*sin |- ------------ + ------------|        cosh |- ------------ + ------------|*sinh |- ------------ + ------------|  |
       |   2|  \/ 30 *im(t)   \/ 30 *im(c)|       2|  \/ 30 *re(t)   \/ 30 *re(c)|| |       \       30             30     /     \       30             30     /             \       30             30     /      \       30             30     /  |   |   2|  \/ 30 *im(t)   \/ 30 *im(c)|       2|  \/ 30 *re(t)   \/ 30 *re(c)|| |       \       30             30     /     \       30             30     /             \       30             30     /      \       30             30     /  |
       |cos |- ------------ + ------------| + sinh |- ------------ + ------------||*|----------------------------------------------------------------------------- + -----------------------------------------------------------------------------|   |cos |- ------------ + ------------| + sinh |- ------------ + ------------||*|----------------------------------------------------------------------------- + -----------------------------------------------------------------------------|
       \    \       30             30     /        \       30             30     // |                                                                            2                                                                               2|   \    \       30             30     /        \       30             30     // |                                                                            2                                                                               2|
                                                                                    |/    /    ____           ____      \        /    ____           ____      \\    /    /    ____           ____      \        /    ____           ____      \\ |                                                                                |/    /    ____           ____      \        /    ____           ____      \\    /    /    ____           ____      \        /    ____           ____      \\ |
                                                                                    ||   2|  \/ 30 *im(t)   \/ 30 *im(c)|       2|  \/ 30 *re(t)   \/ 30 *re(c)||    |   2|  \/ 30 *im(t)   \/ 30 *im(c)|       2|  \/ 30 *re(t)   \/ 30 *re(c)|| |                                                                                ||   2|  \/ 30 *im(t)   \/ 30 *im(c)|       2|  \/ 30 *re(t)   \/ 30 *re(c)||    |   2|  \/ 30 *im(t)   \/ 30 *im(c)|       2|  \/ 30 *re(t)   \/ 30 *re(c)|| |
                                                                                    ||cos |- ------------ + ------------| + sinh |- ------------ + ------------||    |cos |- ------------ + ------------| + sinh |- ------------ + ------------|| |                                                                                ||cos |- ------------ + ------------| + sinh |- ------------ + ------------||    |cos |- ------------ + ------------| + sinh |- ------------ + ------------|| |
                                                                                    \\    \       30             30     /        \       30             30     //    \    \       30             30     /        \       30             30     // /                                                                                \\    \       30             30     /        \       30             30     //    \    \       30             30     /        \       30             30     // /
$$x_{1} = \frac{10 \sqrt{30} i \sin{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} \cos{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)}}{\left(\frac{\sin^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} \cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)}}{\left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)} \cosh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}}{\left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)^{2}}\right) \left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)} - \frac{10 \sqrt{30} \sinh{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)} \cosh{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}}{\left(\frac{\sin^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} \cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)}}{\left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)} \cosh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}}{\left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)^{2}}\right) \left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)}$$
x1 = 10*sqrt(30)*i*sin(sqrt(30)*im(c)/30 - sqrt(30)*im(t)/30)*cos(sqrt(30)*im(c)/30 - sqrt(30)*im(t)/30)/((sin(sqrt(30)*im(c)/30 - sqrt(30)*im(t)/30)^2*cos(sqrt(30)*im(c)/30 - sqrt(30)*im(t)/30)^2/(cos(sqrt(30)*im(c)/30 - sqrt(30)*im(t)/30)^2 + sinh(sqrt(30)*re(c)/30 - sqrt(30)*re(t)/30)^2)^2 + sinh(sqrt(30)*re(c)/30 - sqrt(30)*re(t)/30)^2*cosh(sqrt(30)*re(c)/30 - sqrt(30)*re(t)/30)^2/(cos(sqrt(30)*im(c)/30 - sqrt(30)*im(t)/30)^2 + sinh(sqrt(30)*re(c)/30 - sqrt(30)*re(t)/30)^2)^2)*(cos(sqrt(30)*im(c)/30 - sqrt(30)*im(t)/30)^2 + sinh(sqrt(30)*re(c)/30 - sqrt(30)*re(t)/30)^2)) - 10*sqrt(30)*sinh(sqrt(30)*re(c)/30 - sqrt(30)*re(t)/30)*cosh(sqrt(30)*re(c)/30 - sqrt(30)*re(t)/30)/((sin(sqrt(30)*im(c)/30 - sqrt(30)*im(t)/30)^2*cos(sqrt(30)*im(c)/30 - sqrt(30)*im(t)/30)^2/(cos(sqrt(30)*im(c)/30 - sqrt(30)*im(t)/30)^2 + sinh(sqrt(30)*re(c)/30 - sqrt(30)*re(t)/30)^2)^2 + sinh(sqrt(30)*re(c)/30 - sqrt(30)*re(t)/30)^2*cosh(sqrt(30)*re(c)/30 - sqrt(30)*re(t)/30)^2/(cos(sqrt(30)*im(c)/30 - sqrt(30)*im(t)/30)^2 + sinh(sqrt(30)*re(c)/30 - sqrt(30)*re(t)/30)^2)^2)*(cos(sqrt(30)*im(c)/30 - sqrt(30)*im(t)/30)^2 + sinh(sqrt(30)*re(c)/30 - sqrt(30)*re(t)/30)^2))
Suma y producto de raíces [src]
suma
                                                                                             /    ____           ____      \     /    ____           ____      \                                                                                                                                                                             /    ____           ____      \    /    ____           ____      \                                                                              
                                                                                    ____     |  \/ 30 *re(t)   \/ 30 *re(c)|     |  \/ 30 *re(t)   \/ 30 *re(c)|                                                                                                                                                                     ____    |  \/ 30 *im(t)   \/ 30 *im(c)|    |  \/ 30 *im(t)   \/ 30 *im(c)|                                                                              
                                                                               10*\/ 30 *cosh|- ------------ + ------------|*sinh|- ------------ + ------------|                                                                                                                                                              10*I*\/ 30 *cos|- ------------ + ------------|*sin|- ------------ + ------------|                                                                              
                                                                                             \       30             30     /     \       30             30     /                                                                                                                                                                             \       30             30     /    \       30             30     /                                                                              
- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                               /       /    ____           ____      \     /    ____           ____      \             /    ____           ____      \      /    ____           ____      \  \                                                                                /       /    ____           ____      \     /    ____           ____      \             /    ____           ____      \      /    ____           ____      \  \
                                                                               |      2|  \/ 30 *im(t)   \/ 30 *im(c)|    2|  \/ 30 *im(t)   \/ 30 *im(c)|            2|  \/ 30 *re(t)   \/ 30 *re(c)|     2|  \/ 30 *re(t)   \/ 30 *re(c)|  |                                                                                |      2|  \/ 30 *im(t)   \/ 30 *im(c)|    2|  \/ 30 *im(t)   \/ 30 *im(c)|            2|  \/ 30 *re(t)   \/ 30 *re(c)|     2|  \/ 30 *re(t)   \/ 30 *re(c)|  |
  /    /    ____           ____      \        /    ____           ____      \\ |   cos |- ------------ + ------------|*sin |- ------------ + ------------|        cosh |- ------------ + ------------|*sinh |- ------------ + ------------|  |   /    /    ____           ____      \        /    ____           ____      \\ |   cos |- ------------ + ------------|*sin |- ------------ + ------------|        cosh |- ------------ + ------------|*sinh |- ------------ + ------------|  |
  |   2|  \/ 30 *im(t)   \/ 30 *im(c)|       2|  \/ 30 *re(t)   \/ 30 *re(c)|| |       \       30             30     /     \       30             30     /             \       30             30     /      \       30             30     /  |   |   2|  \/ 30 *im(t)   \/ 30 *im(c)|       2|  \/ 30 *re(t)   \/ 30 *re(c)|| |       \       30             30     /     \       30             30     /             \       30             30     /      \       30             30     /  |
  |cos |- ------------ + ------------| + sinh |- ------------ + ------------||*|----------------------------------------------------------------------------- + -----------------------------------------------------------------------------|   |cos |- ------------ + ------------| + sinh |- ------------ + ------------||*|----------------------------------------------------------------------------- + -----------------------------------------------------------------------------|
  \    \       30             30     /        \       30             30     // |                                                                            2                                                                               2|   \    \       30             30     /        \       30             30     // |                                                                            2                                                                               2|
                                                                               |/    /    ____           ____      \        /    ____           ____      \\    /    /    ____           ____      \        /    ____           ____      \\ |                                                                                |/    /    ____           ____      \        /    ____           ____      \\    /    /    ____           ____      \        /    ____           ____      \\ |
                                                                               ||   2|  \/ 30 *im(t)   \/ 30 *im(c)|       2|  \/ 30 *re(t)   \/ 30 *re(c)||    |   2|  \/ 30 *im(t)   \/ 30 *im(c)|       2|  \/ 30 *re(t)   \/ 30 *re(c)|| |                                                                                ||   2|  \/ 30 *im(t)   \/ 30 *im(c)|       2|  \/ 30 *re(t)   \/ 30 *re(c)||    |   2|  \/ 30 *im(t)   \/ 30 *im(c)|       2|  \/ 30 *re(t)   \/ 30 *re(c)|| |
                                                                               ||cos |- ------------ + ------------| + sinh |- ------------ + ------------||    |cos |- ------------ + ------------| + sinh |- ------------ + ------------|| |                                                                                ||cos |- ------------ + ------------| + sinh |- ------------ + ------------||    |cos |- ------------ + ------------| + sinh |- ------------ + ------------|| |
                                                                               \\    \       30             30     /        \       30             30     //    \    \       30             30     /        \       30             30     // /                                                                                \\    \       30             30     /        \       30             30     //    \    \       30             30     /        \       30             30     // /
$$\frac{10 \sqrt{30} i \sin{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} \cos{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)}}{\left(\frac{\sin^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} \cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)}}{\left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)} \cosh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}}{\left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)^{2}}\right) \left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)} - \frac{10 \sqrt{30} \sinh{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)} \cosh{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}}{\left(\frac{\sin^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} \cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)}}{\left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)} \cosh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}}{\left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)^{2}}\right) \left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)}$$
=
                                                                                             /    ____           ____      \     /    ____           ____      \                                                                                                                                                                             /    ____           ____      \    /    ____           ____      \                                                                              
                                                                                    ____     |  \/ 30 *re(t)   \/ 30 *re(c)|     |  \/ 30 *re(t)   \/ 30 *re(c)|                                                                                                                                                                     ____    |  \/ 30 *im(t)   \/ 30 *im(c)|    |  \/ 30 *im(t)   \/ 30 *im(c)|                                                                              
                                                                               10*\/ 30 *cosh|- ------------ + ------------|*sinh|- ------------ + ------------|                                                                                                                                                              10*I*\/ 30 *cos|- ------------ + ------------|*sin|- ------------ + ------------|                                                                              
                                                                                             \       30             30     /     \       30             30     /                                                                                                                                                                             \       30             30     /    \       30             30     /                                                                              
- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                               /       /    ____           ____      \     /    ____           ____      \             /    ____           ____      \      /    ____           ____      \  \                                                                                /       /    ____           ____      \     /    ____           ____      \             /    ____           ____      \      /    ____           ____      \  \
                                                                               |      2|  \/ 30 *im(t)   \/ 30 *im(c)|    2|  \/ 30 *im(t)   \/ 30 *im(c)|            2|  \/ 30 *re(t)   \/ 30 *re(c)|     2|  \/ 30 *re(t)   \/ 30 *re(c)|  |                                                                                |      2|  \/ 30 *im(t)   \/ 30 *im(c)|    2|  \/ 30 *im(t)   \/ 30 *im(c)|            2|  \/ 30 *re(t)   \/ 30 *re(c)|     2|  \/ 30 *re(t)   \/ 30 *re(c)|  |
  /    /    ____           ____      \        /    ____           ____      \\ |   cos |- ------------ + ------------|*sin |- ------------ + ------------|        cosh |- ------------ + ------------|*sinh |- ------------ + ------------|  |   /    /    ____           ____      \        /    ____           ____      \\ |   cos |- ------------ + ------------|*sin |- ------------ + ------------|        cosh |- ------------ + ------------|*sinh |- ------------ + ------------|  |
  |   2|  \/ 30 *im(t)   \/ 30 *im(c)|       2|  \/ 30 *re(t)   \/ 30 *re(c)|| |       \       30             30     /     \       30             30     /             \       30             30     /      \       30             30     /  |   |   2|  \/ 30 *im(t)   \/ 30 *im(c)|       2|  \/ 30 *re(t)   \/ 30 *re(c)|| |       \       30             30     /     \       30             30     /             \       30             30     /      \       30             30     /  |
  |cos |- ------------ + ------------| + sinh |- ------------ + ------------||*|----------------------------------------------------------------------------- + -----------------------------------------------------------------------------|   |cos |- ------------ + ------------| + sinh |- ------------ + ------------||*|----------------------------------------------------------------------------- + -----------------------------------------------------------------------------|
  \    \       30             30     /        \       30             30     // |                                                                            2                                                                               2|   \    \       30             30     /        \       30             30     // |                                                                            2                                                                               2|
                                                                               |/    /    ____           ____      \        /    ____           ____      \\    /    /    ____           ____      \        /    ____           ____      \\ |                                                                                |/    /    ____           ____      \        /    ____           ____      \\    /    /    ____           ____      \        /    ____           ____      \\ |
                                                                               ||   2|  \/ 30 *im(t)   \/ 30 *im(c)|       2|  \/ 30 *re(t)   \/ 30 *re(c)||    |   2|  \/ 30 *im(t)   \/ 30 *im(c)|       2|  \/ 30 *re(t)   \/ 30 *re(c)|| |                                                                                ||   2|  \/ 30 *im(t)   \/ 30 *im(c)|       2|  \/ 30 *re(t)   \/ 30 *re(c)||    |   2|  \/ 30 *im(t)   \/ 30 *im(c)|       2|  \/ 30 *re(t)   \/ 30 *re(c)|| |
                                                                               ||cos |- ------------ + ------------| + sinh |- ------------ + ------------||    |cos |- ------------ + ------------| + sinh |- ------------ + ------------|| |                                                                                ||cos |- ------------ + ------------| + sinh |- ------------ + ------------||    |cos |- ------------ + ------------| + sinh |- ------------ + ------------|| |
                                                                               \\    \       30             30     /        \       30             30     //    \    \       30             30     /        \       30             30     // /                                                                                \\    \       30             30     /        \       30             30     //    \    \       30             30     /        \       30             30     // /
$$\frac{10 \sqrt{30} i \sin{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} \cos{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)}}{\left(\frac{\sin^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} \cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)}}{\left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)} \cosh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}}{\left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)^{2}}\right) \left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)} - \frac{10 \sqrt{30} \sinh{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)} \cosh{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}}{\left(\frac{\sin^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} \cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)}}{\left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)} \cosh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}}{\left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)^{2}}\right) \left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)}$$
producto
                                                                                             /    ____           ____      \     /    ____           ____      \                                                                                                                                                                             /    ____           ____      \    /    ____           ____      \                                                                              
                                                                                    ____     |  \/ 30 *re(t)   \/ 30 *re(c)|     |  \/ 30 *re(t)   \/ 30 *re(c)|                                                                                                                                                                     ____    |  \/ 30 *im(t)   \/ 30 *im(c)|    |  \/ 30 *im(t)   \/ 30 *im(c)|                                                                              
                                                                               10*\/ 30 *cosh|- ------------ + ------------|*sinh|- ------------ + ------------|                                                                                                                                                              10*I*\/ 30 *cos|- ------------ + ------------|*sin|- ------------ + ------------|                                                                              
                                                                                             \       30             30     /     \       30             30     /                                                                                                                                                                             \       30             30     /    \       30             30     /                                                                              
- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                               /       /    ____           ____      \     /    ____           ____      \             /    ____           ____      \      /    ____           ____      \  \                                                                                /       /    ____           ____      \     /    ____           ____      \             /    ____           ____      \      /    ____           ____      \  \
                                                                               |      2|  \/ 30 *im(t)   \/ 30 *im(c)|    2|  \/ 30 *im(t)   \/ 30 *im(c)|            2|  \/ 30 *re(t)   \/ 30 *re(c)|     2|  \/ 30 *re(t)   \/ 30 *re(c)|  |                                                                                |      2|  \/ 30 *im(t)   \/ 30 *im(c)|    2|  \/ 30 *im(t)   \/ 30 *im(c)|            2|  \/ 30 *re(t)   \/ 30 *re(c)|     2|  \/ 30 *re(t)   \/ 30 *re(c)|  |
  /    /    ____           ____      \        /    ____           ____      \\ |   cos |- ------------ + ------------|*sin |- ------------ + ------------|        cosh |- ------------ + ------------|*sinh |- ------------ + ------------|  |   /    /    ____           ____      \        /    ____           ____      \\ |   cos |- ------------ + ------------|*sin |- ------------ + ------------|        cosh |- ------------ + ------------|*sinh |- ------------ + ------------|  |
  |   2|  \/ 30 *im(t)   \/ 30 *im(c)|       2|  \/ 30 *re(t)   \/ 30 *re(c)|| |       \       30             30     /     \       30             30     /             \       30             30     /      \       30             30     /  |   |   2|  \/ 30 *im(t)   \/ 30 *im(c)|       2|  \/ 30 *re(t)   \/ 30 *re(c)|| |       \       30             30     /     \       30             30     /             \       30             30     /      \       30             30     /  |
  |cos |- ------------ + ------------| + sinh |- ------------ + ------------||*|----------------------------------------------------------------------------- + -----------------------------------------------------------------------------|   |cos |- ------------ + ------------| + sinh |- ------------ + ------------||*|----------------------------------------------------------------------------- + -----------------------------------------------------------------------------|
  \    \       30             30     /        \       30             30     // |                                                                            2                                                                               2|   \    \       30             30     /        \       30             30     // |                                                                            2                                                                               2|
                                                                               |/    /    ____           ____      \        /    ____           ____      \\    /    /    ____           ____      \        /    ____           ____      \\ |                                                                                |/    /    ____           ____      \        /    ____           ____      \\    /    /    ____           ____      \        /    ____           ____      \\ |
                                                                               ||   2|  \/ 30 *im(t)   \/ 30 *im(c)|       2|  \/ 30 *re(t)   \/ 30 *re(c)||    |   2|  \/ 30 *im(t)   \/ 30 *im(c)|       2|  \/ 30 *re(t)   \/ 30 *re(c)|| |                                                                                ||   2|  \/ 30 *im(t)   \/ 30 *im(c)|       2|  \/ 30 *re(t)   \/ 30 *re(c)||    |   2|  \/ 30 *im(t)   \/ 30 *im(c)|       2|  \/ 30 *re(t)   \/ 30 *re(c)|| |
                                                                               ||cos |- ------------ + ------------| + sinh |- ------------ + ------------||    |cos |- ------------ + ------------| + sinh |- ------------ + ------------|| |                                                                                ||cos |- ------------ + ------------| + sinh |- ------------ + ------------||    |cos |- ------------ + ------------| + sinh |- ------------ + ------------|| |
                                                                               \\    \       30             30     /        \       30             30     //    \    \       30             30     /        \       30             30     // /                                                                                \\    \       30             30     /        \       30             30     //    \    \       30             30     /        \       30             30     // /
$$\frac{10 \sqrt{30} i \sin{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} \cos{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)}}{\left(\frac{\sin^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} \cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)}}{\left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)} \cosh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}}{\left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)^{2}}\right) \left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)} - \frac{10 \sqrt{30} \sinh{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)} \cosh{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}}{\left(\frac{\sin^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} \cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)}}{\left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)} \cosh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}}{\left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)^{2}}\right) \left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)}$$
=
                                                                           /     /  ____                 \                                                              \
                                                                           |     |\/ 30 *(-im(t) + im(c))|                                                              |
          /    /  ____                 \        /  ____                 \\ |I*sin|-----------------------|       /  ____                 \     /  ____                 \|
     ____ |   2|\/ 30 *(-im(t) + im(c))|       2|\/ 30 *(-re(t) + re(c))|| |     \           15          /       |\/ 30 *(-re(t) + re(c))|     |\/ 30 *(-re(t) + re(c))||
10*\/ 30 *|cos |-----------------------| + sinh |-----------------------||*|------------------------------ - cosh|-----------------------|*sinh|-----------------------||
          \    \           30          /        \           30          // \              2                      \           30          /     \           30          //
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                           /  ____                 \     /  ____                 \        /  ____                 \      /  ____                 \                       
                          2|\/ 30 *(-im(t) + im(c))|    2|\/ 30 *(-im(t) + im(c))|       2|\/ 30 *(-re(t) + re(c))|     2|\/ 30 *(-re(t) + re(c))|                       
                       cos |-----------------------|*sin |-----------------------| + cosh |-----------------------|*sinh |-----------------------|                       
                           \           30          /     \           30          /        \           30          /      \           30          /                       
$$\frac{10 \sqrt{30} \left(\frac{i \sin{\left(\frac{\sqrt{30} \left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(t\right)}\right)}{15} \right)}}{2} - \sinh{\left(\frac{\sqrt{30} \left(\operatorname{re}{\left(c\right)} - \operatorname{re}{\left(t\right)}\right)}{30} \right)} \cosh{\left(\frac{\sqrt{30} \left(\operatorname{re}{\left(c\right)} - \operatorname{re}{\left(t\right)}\right)}{30} \right)}\right) \left(\cos^{2}{\left(\frac{\sqrt{30} \left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(t\right)}\right)}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \left(\operatorname{re}{\left(c\right)} - \operatorname{re}{\left(t\right)}\right)}{30} \right)}\right)}{\sin^{2}{\left(\frac{\sqrt{30} \left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(t\right)}\right)}{30} \right)} \cos^{2}{\left(\frac{\sqrt{30} \left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(t\right)}\right)}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \left(\operatorname{re}{\left(c\right)} - \operatorname{re}{\left(t\right)}\right)}{30} \right)} \cosh^{2}{\left(\frac{\sqrt{30} \left(\operatorname{re}{\left(c\right)} - \operatorname{re}{\left(t\right)}\right)}{30} \right)}}$$
10*sqrt(30)*(cos(sqrt(30)*(-im(t) + im(c))/30)^2 + sinh(sqrt(30)*(-re(t) + re(c))/30)^2)*(i*sin(sqrt(30)*(-im(t) + im(c))/15)/2 - cosh(sqrt(30)*(-re(t) + re(c))/30)*sinh(sqrt(30)*(-re(t) + re(c))/30))/(cos(sqrt(30)*(-im(t) + im(c))/30)^2*sin(sqrt(30)*(-im(t) + im(c))/30)^2 + cosh(sqrt(30)*(-re(t) + re(c))/30)^2*sinh(sqrt(30)*(-re(t) + re(c))/30)^2)