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Simplificación de expresiones/ Descomposición en fracciones simples/ tan(x)^(cos(sqrt(x))^3)*(cos(sqrt(x))^3*(1+tan(x)^2)/tan(x)-3*cos(sqrt(x))^2*log(tan(x))*sin(sqrt(x))/(2*sqrt(x)))

¿Cómo vas a descomponer esta tan(x)^(cos(sqrt(x))^3)*(cos(sqrt(x))^3*(1+tan(x)^2)/tan(x)-3*cos(sqrt(x))^2*log(tan(x))*sin(sqrt(x))/(2*sqrt(x))) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
           3/  ___\ /   3/  ___\ /       2   \        2/  ___\                /  ___\\
        cos \\/ x / |cos \\/ x /*\1 + tan (x)/   3*cos \\/ x /*log(tan(x))*sin\\/ x /|
(tan(x))           *|------------------------- - ------------------------------------|
                    |          tan(x)                              ___               |
                    \                                          2*\/ x                /
$$\left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \cos^{3}{\left(\sqrt{x} \right)}}{\tan{\left(x \right)}} - \frac{\log{\left(\tan{\left(x \right)} \right)} 3 \cos^{2}{\left(\sqrt{x} \right)} \sin{\left(\sqrt{x} \right)}}{2 \sqrt{x}}\right) \tan^{\cos^{3}{\left(\sqrt{x} \right)}}{\left(x \right)}$$ 
tan(x)^(cos(sqrt(x))^3)*((cos(sqrt(x))^3*(1 + tan(x)^2))/tan(x) - ((3*cos(sqrt(x))^2)*log(tan(x)))*sin(sqrt(x))/(2*sqrt(x)))
Simplificación general [src] 
                            3/  ___\ /  ___    /  ___\                    /  ___\       \
   2/  ___\         -1 + cos \\/ x / |\/ x *cos\\/ x /   3*log(tan(x))*sin\\/ x /*tan(x)|
cos \\/ x /*(tan(x))                *|---------------- - -------------------------------|
                                     |       2                          2               |
                                     \    cos (x)                                       /
-----------------------------------------------------------------------------------------
                                            ___                                          
                                          \/ x
$$\frac{\left(\frac{\sqrt{x} \cos{\left(\sqrt{x} \right)}}{\cos^{2}{\left(x \right)}} - \frac{3 \log{\left(\tan{\left(x \right)} \right)} \sin{\left(\sqrt{x} \right)} \tan{\left(x \right)}}{2}\right) \cos^{2}{\left(\sqrt{x} \right)} \tan^{\cos^{3}{\left(\sqrt{x} \right)} - 1}{\left(x \right)}}{\sqrt{x}}$$ 
cos(sqrt(x))^2*tan(x)^(-1 + cos(sqrt(x))^3)*(sqrt(x)*cos(sqrt(x))/cos(x)^2 - 3*log(tan(x))*sin(sqrt(x))*tan(x)/2)/sqrt(x)
Respuesta numérica [src] 
tan(x)^(cos(sqrt(x))^3)*(cos(sqrt(x))^3*(1.0 + tan(x)^2)/tan(x) - 1.5*x^(-0.5)*cos(sqrt(x))^2*log(tan(x))*sin(sqrt(x)))
tan(x)^(cos(sqrt(x))^3)*(cos(sqrt(x))^3*(1.0 + tan(x)^2)/tan(x) - 1.5*x^(-0.5)*cos(sqrt(x))^2*log(tan(x))*sin(sqrt(x)))
Potencias [src] 
           3/  ___\ /   3/  ___\ /       2   \        2/  ___\                /  ___\\
        cos \\/ x / |cos \\/ x /*\1 + tan (x)/   3*cos \\/ x /*log(tan(x))*sin\\/ x /|
(tan(x))           *|------------------------- - ------------------------------------|
                    |          tan(x)                              ___               |
                    \                                          2*\/ x                /
$$\left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \cos^{3}{\left(\sqrt{x} \right)}}{\tan{\left(x \right)}} - \frac{3 \log{\left(\tan{\left(x \right)} \right)} \sin{\left(\sqrt{x} \right)} \cos^{2}{\left(\sqrt{x} \right)}}{2 \sqrt{x}}\right) \tan^{\cos^{3}{\left(\sqrt{x} \right)}}{\left(x \right)}$$ 
                    /                      3\ /                          3                                                                                                                      \
                    |/     ___         ___\ | |    /     ___         ___\  /                    2\                                            2                                                 |
                    || I*\/ x     -I*\/ x | | |    | I*\/ x     -I*\/ x |  |    /   I*x    -I*x\ |                      /     ___         ___\                                                  |
                    ||e          e        | | |    |e          e        |  |    \- e    + e    / | / I*x    -I*x\       | I*\/ x     -I*\/ x |  /        ___        ___\    /  /   I*x    -I*x\\|
                    ||-------- + ---------| | |  I*|-------- + ---------| *|1 - -----------------|*\e    + e    /       |e          e        |  |   -I*\/ x     I*\/ x |    |I*\- e    + e    /||
                    \\   2           2    / / |    \   2           2    /  |                   2 |                  3*I*|-------- + ---------| *\- e         + e       /*log|------------------||
/  /   I*x    -I*x\\                          |                            |     / I*x    -I*x\  |                      \   2           2    /                              |    I*x    -I*x   ||
|I*\- e    + e    /|                          |                            \     \e    + e    /  /                                                                          \   e    + e       /|
|------------------|                         *|- ---------------------------------------------------------------- + ----------------------------------------------------------------------------|
|    I*x    -I*x   |                          |                              I*x    -I*x                                                                  ___                                   |
\   e    + e       /                          \                           - e    + e                                                                  4*\/ x                                    /
$$\left(\frac{i \left(- e^{i x} + e^{- i x}\right)}{e^{i x} + e^{- i x}}\right)^{\left(\frac{e^{i \sqrt{x}}}{2} + \frac{e^{- i \sqrt{x}}}{2}\right)^{3}} \left(- \frac{i \left(- \frac{\left(- e^{i x} + e^{- i x}\right)^{2}}{\left(e^{i x} + e^{- i x}\right)^{2}} + 1\right) \left(\frac{e^{i \sqrt{x}}}{2} + \frac{e^{- i \sqrt{x}}}{2}\right)^{3} \left(e^{i x} + e^{- i x}\right)}{- e^{i x} + e^{- i x}} + \frac{3 i \left(\frac{e^{i \sqrt{x}}}{2} + \frac{e^{- i \sqrt{x}}}{2}\right)^{2} \left(e^{i \sqrt{x}} - e^{- i \sqrt{x}}\right) \log{\left(\frac{i \left(- e^{i x} + e^{- i x}\right)}{e^{i x} + e^{- i x}} \right)}}{4 \sqrt{x}}\right)$$ 
(i*(-exp(i*x) + exp(-i*x))/(exp(i*x) + exp(-i*x)))^((exp(i*sqrt(x))/2 + exp(-i*sqrt(x))/2)^3)*(-i*(exp(i*sqrt(x))/2 + exp(-i*sqrt(x))/2)^3*(1 - (-exp(i*x) + exp(-i*x))^2/(exp(i*x) + exp(-i*x))^2)*(exp(i*x) + exp(-i*x))/(-exp(i*x) + exp(-i*x)) + 3*i*(exp(i*sqrt(x))/2 + exp(-i*sqrt(x))/2)^2*(-exp(-i*sqrt(x)) + exp(i*sqrt(x)))*log(i*(-exp(i*x) + exp(-i*x))/(exp(i*x) + exp(-i*x)))/(4*sqrt(x)))
Denominador racional [src] 
                                    3/  ___\                                               3/  ___\                                 3/  ___\                              
    ___    3/  ___\         -1 + cos \\/ x /       ___    3/  ___\    2            -1 + cos \\/ x /        2/  ___\         -1 + cos \\/ x /                /  ___\       
2*\/ x *cos \\/ x /*(tan(x))                 + 2*\/ x *cos \\/ x /*tan (x)*(tan(x))                 - 3*cos \\/ x /*(tan(x))                *log(tan(x))*sin\\/ x /*tan(x)
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                     ___                                                                                  
                                                                                 2*\/ x
$$\frac{2 \sqrt{x} \cos^{3}{\left(\sqrt{x} \right)} \tan^{2}{\left(x \right)} \tan^{\cos^{3}{\left(\sqrt{x} \right)} - 1}{\left(x \right)} + 2 \sqrt{x} \cos^{3}{\left(\sqrt{x} \right)} \tan^{\cos^{3}{\left(\sqrt{x} \right)} - 1}{\left(x \right)} - 3 \log{\left(\tan{\left(x \right)} \right)} \sin{\left(\sqrt{x} \right)} \cos^{2}{\left(\sqrt{x} \right)} \tan{\left(x \right)} \tan^{\cos^{3}{\left(\sqrt{x} \right)} - 1}{\left(x \right)}}{2 \sqrt{x}}$$ 
(2*sqrt(x)*cos(sqrt(x))^3*tan(x)^(-1 + cos(sqrt(x))^3) + 2*sqrt(x)*cos(sqrt(x))^3*tan(x)^2*tan(x)^(-1 + cos(sqrt(x))^3) - 3*cos(sqrt(x))^2*tan(x)^(-1 + cos(sqrt(x))^3)*log(tan(x))*sin(sqrt(x))*tan(x))/(2*sqrt(x))
Denominador común [src] 
                                                                        3/  ___\                            3/  ___\                              
                       3/  ___\              ___    3/  ___\         cos \\/ x /        2/  ___\         cos \\/ x /                /  ___\       
   3/  ___\         cos \\/ x /          2*\/ x *cos \\/ x /*(tan(x))            - 3*cos \\/ x /*(tan(x))           *log(tan(x))*sin\\/ x /*tan(x)
cos \\/ x /*(tan(x))           *tan(x) + ---------------------------------------------------------------------------------------------------------
                                                                                           ___                                                    
                                                                                       2*\/ x *tan(x)
$$\cos^{3}{\left(\sqrt{x} \right)} \tan{\left(x \right)} \tan^{\cos^{3}{\left(\sqrt{x} \right)}}{\left(x \right)} + \frac{2 \sqrt{x} \cos^{3}{\left(\sqrt{x} \right)} \tan^{\cos^{3}{\left(\sqrt{x} \right)}}{\left(x \right)} - 3 \log{\left(\tan{\left(x \right)} \right)} \sin{\left(\sqrt{x} \right)} \cos^{2}{\left(\sqrt{x} \right)} \tan{\left(x \right)} \tan^{\cos^{3}{\left(\sqrt{x} \right)}}{\left(x \right)}}{2 \sqrt{x} \tan{\left(x \right)}}$$ 
cos(sqrt(x))^3*tan(x)^(cos(sqrt(x))^3)*tan(x) + (2*sqrt(x)*cos(sqrt(x))^3*tan(x)^(cos(sqrt(x))^3) - 3*cos(sqrt(x))^2*tan(x)^(cos(sqrt(x))^3)*log(tan(x))*sin(sqrt(x))*tan(x))/(2*sqrt(x)*tan(x))
Combinatoria [src] 
                       3/  ___\                                                                                    
   2/  ___\         cos \\/ x / /    ___    /  ___\                    /  ___\              ___    2       /  ___\\
cos \\/ x /*(tan(x))           *\2*\/ x *cos\\/ x / - 3*log(tan(x))*sin\\/ x /*tan(x) + 2*\/ x *tan (x)*cos\\/ x //
-------------------------------------------------------------------------------------------------------------------
                                                       ___                                                         
                                                   2*\/ x *tan(x)
$$\frac{\left(2 \sqrt{x} \cos{\left(\sqrt{x} \right)} \tan^{2}{\left(x \right)} + 2 \sqrt{x} \cos{\left(\sqrt{x} \right)} - 3 \log{\left(\tan{\left(x \right)} \right)} \sin{\left(\sqrt{x} \right)} \tan{\left(x \right)}\right) \cos^{2}{\left(\sqrt{x} \right)} \tan^{\cos^{3}{\left(\sqrt{x} \right)}}{\left(x \right)}}{2 \sqrt{x} \tan{\left(x \right)}}$$ 
cos(sqrt(x))^2*tan(x)^(cos(sqrt(x))^3)*(2*sqrt(x)*cos(sqrt(x)) - 3*log(tan(x))*sin(sqrt(x))*tan(x) + 2*sqrt(x)*tan(x)^2*cos(sqrt(x)))/(2*sqrt(x)*tan(x))
Abrimos la expresión [src] 
                       3/  ___\                                                                     3/  ___\                       
   3/  ___\         cos \\/ x /                          3/  ___\               2/  ___\         cos \\/ x /                /  ___\
cos \\/ x /*(tan(x))                 3/  ___\         cos \\/ x /          3*cos \\/ x /*(tan(x))           *log(tan(x))*sin\\/ x /
------------------------------- + cos \\/ x /*(tan(x))           *tan(x) - --------------------------------------------------------
             tan(x)                                                                                    ___                         
                                                                                                   2*\/ x
$$\cos^{3}{\left(\sqrt{x} \right)} \tan{\left(x \right)} \tan^{\cos^{3}{\left(\sqrt{x} \right)}}{\left(x \right)} + \frac{\cos^{3}{\left(\sqrt{x} \right)} \tan^{\cos^{3}{\left(\sqrt{x} \right)}}{\left(x \right)}}{\tan{\left(x \right)}} - \frac{3 \log{\left(\tan{\left(x \right)} \right)} \sin{\left(\sqrt{x} \right)} \cos^{2}{\left(\sqrt{x} \right)} \tan^{\cos^{3}{\left(\sqrt{x} \right)}}{\left(x \right)}}{2 \sqrt{x}}$$ 
           3/  ___\ /   3/  ___\ /       2   \        2/  ___\                /  ___\\
        cos \\/ x / |cos \\/ x /*\1 + tan (x)/   3*cos \\/ x /*log(tan(x))*sin\\/ x /|
(tan(x))           *|------------------------- - ------------------------------------|
                    |          tan(x)                              ___               |
                    \                                          2*\/ x                /
$$\left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \cos^{3}{\left(\sqrt{x} \right)}}{\tan{\left(x \right)}} - \frac{3 \log{\left(\tan{\left(x \right)} \right)} \sin{\left(\sqrt{x} \right)} \cos^{2}{\left(\sqrt{x} \right)}}{2 \sqrt{x}}\right) \tan^{\cos^{3}{\left(\sqrt{x} \right)}}{\left(x \right)}$$ 
tan(x)^(cos(sqrt(x))^3)*((cos(sqrt(x))^3*(1 + tan(x)^2))/tan(x) - 3*cos(sqrt(x))^2*log(tan(x))*sin(sqrt(x))/(2*sqrt(x)))
Compilar la expresión [src] 
           3/  ___\ /   3/  ___\ /       2   \        2/  ___\                /  ___\\
        cos \\/ x / |cos \\/ x /*\1 + tan (x)/   3*cos \\/ x /*log(tan(x))*sin\\/ x /|
(tan(x))           *|------------------------- - ------------------------------------|
                    |          tan(x)                              ___               |
                    \                                          2*\/ x                /
$$\left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \cos^{3}{\left(\sqrt{x} \right)}}{\tan{\left(x \right)}} - \frac{3 \log{\left(\tan{\left(x \right)} \right)} \sin{\left(\sqrt{x} \right)} \cos^{2}{\left(\sqrt{x} \right)}}{2 \sqrt{x}}\right) \tan^{\cos^{3}{\left(\sqrt{x} \right)}}{\left(x \right)}$$ 
tan(x)^(cos(sqrt(x))^3)*(cos(sqrt(x))^3*(1 + tan(x)^2)/tan(x) - 3*cos(sqrt(x))^2*log(tan(x))*sin(sqrt(x))/(2*sqrt(x)))
Unión de expresiones racionales [src] 
                       3/  ___\                                                                       
   2/  ___\         cos \\/ x / /                   /  ___\              ___ /       2   \    /  ___\\
cos \\/ x /*(tan(x))           *\- 3*log(tan(x))*sin\\/ x /*tan(x) + 2*\/ x *\1 + tan (x)/*cos\\/ x //
------------------------------------------------------------------------------------------------------
                                                ___                                                   
                                            2*\/ x *tan(x)
$$\frac{\left(2 \sqrt{x} \left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(\sqrt{x} \right)} - 3 \log{\left(\tan{\left(x \right)} \right)} \sin{\left(\sqrt{x} \right)} \tan{\left(x \right)}\right) \cos^{2}{\left(\sqrt{x} \right)} \tan^{\cos^{3}{\left(\sqrt{x} \right)}}{\left(x \right)}}{2 \sqrt{x} \tan{\left(x \right)}}$$ 
cos(sqrt(x))^2*tan(x)^(cos(sqrt(x))^3)*(-3*log(tan(x))*sin(sqrt(x))*tan(x) + 2*sqrt(x)*(1 + tan(x)^2)*cos(sqrt(x)))/(2*sqrt(x)*tan(x))
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