Descomposición de una fracción log(1+tan(x)²)/(-4+4*tan(x)²)-log(1+tan(x))/(-4+4*tan(x)²)-log(-1+tan(x))/(-4+4*tan(x)²)+tan(x)²*log(1+tan(x))/(-4+4*tan(x)²)+tan(x)²*log(-1+tan(x))/(-4+4*tan(x)²)-tan(x)²*log(1+tan(x)²)/(-4+4*tan(x)²)-4*x*tan(x)/(-4+4*tan(x)²) (logaritmo de (1 más tangente de (x) al cuadrado) dividir por (menos 4 más 4 multiplicar por tangente de (x) al cuadrado) menos logaritmo de (1 más tangente de (x)) dividir por (menos 4 más 4 multiplicar por tangente de (x) al cuadrado) menos logaritmo de (menos 1 más tangente de (x)) dividir por (menos 4 más 4 multiplicar por tangente de (x) al cuadrado) más tangente de (x) al cuadrado multiplicar por logaritmo de (1 más tangente de (x)) dividir por (menos 4 más 4 multiplicar por tangente de (x) al cuadrado) más tangente de (x) al cuadrado multiplicar por logaritmo de (menos 1 más tangente de (x)) dividir por (menos 4 más 4 multiplicar por tangente de (x) al cuadrado) menos tangente de (x) al cuadrado multiplicar por logaritmo de (1 más tangente de (x) al cuadrado) dividir por (menos 4 más 4 multiplicar por tangente de (x) al cuadrado) menos 4 multiplicar por x multiplicar por tangente de (x) dividir por (menos 4 más 4 multiplicar por tangente de (x) al cuadrado))

Ha introducido [src]

   /       2   \                                           2                         2                          2       /       2   \                 
log\1 + tan (x)/   log(1 + tan(x))   log(-1 + tan(x))   tan (x)*log(1 + tan(x))   tan (x)*log(-1 + tan(x))   tan (x)*log\1 + tan (x)/     4*x*tan(x)  
---------------- - --------------- - ---------------- + ----------------------- + ------------------------ - ------------------------ - --------------
           2                  2                 2                      2                         2                          2                     2   
 -4 + 4*tan (x)     -4 + 4*tan (x)    -4 + 4*tan (x)         -4 + 4*tan (x)            -4 + 4*tan (x)             -4 + 4*tan (x)        -4 + 4*tan (x)

- \frac{4 x \tan{\left(x \right)}}{4 \tan^{2}{\left(x \right)} - 4} + \left(- \frac{\log{\left(\tan^{2}{\left(x \right)} + 1 \right)} \tan^{2}{\left(x \right)}}{4 \tan^{2}{\left(x \right)} - 4} + \left(\frac{\log{\left(\tan{\left(x \right)} - 1 \right)} \tan^{2}{\left(x \right)}}{4 \tan^{2}{\left(x \right)} - 4} + \left(\frac{\log{\left(\tan{\left(x \right)} + 1 \right)} \tan^{2}{\left(x \right)}}{4 \tan^{2}{\left(x \right)} - 4} + \left(\left(- \frac{\log{\left(\tan{\left(x \right)} + 1 \right)}}{4 \tan^{2}{\left(x \right)} - 4} + \frac{\log{\left(\tan^{2}{\left(x \right)} + 1 \right)}}{4 \tan^{2}{\left(x \right)} - 4}\right) - \frac{\log{\left(\tan{\left(x \right)} - 1 \right)}}{4 \tan^{2}{\left(x \right)} - 4}\right)\right)\right)\right)

log(1 + tan(x)^2)/(-4 + 4*tan(x)^2) - log(1 + tan(x))/(-4 + 4*tan(x)^2) - log(-1 + tan(x))/(-4 + 4*tan(x)^2) + (tan(x)^2*log(1 + tan(x)))/(-4 + 4*tan(x)^2) + (tan(x)^2*log(-1 + tan(x)))/(-4 + 4*tan(x)^2) - tan(x)^2*log(1 + tan(x)^2)/(-4 + 4*tan(x)^2) - (4*x)*tan(x)/(-4 + 4*tan(x)^2)

Simplificación general [src]

                                         2                         2                          2       /   1   \                   /   1   \
-log(1 + tan(x)) - log(-1 + tan(x)) + tan (x)*log(1 + tan(x)) + tan (x)*log(-1 + tan(x)) - tan (x)*log|-------| - 4*x*tan(x) + log|-------|
                                                                                                      |   2   |                   |   2   |
                                                                                                      \cos (x)/                   \cos (x)/
-------------------------------------------------------------------------------------------------------------------------------------------
                                                                /        2   \                                                             
                                                              4*\-1 + tan (x)/

\frac{- 4 x \tan{\left(x \right)} + \log{\left(\tan{\left(x \right)} - 1 \right)} \tan^{2}{\left(x \right)} - \log{\left(\tan{\left(x \right)} - 1 \right)} + \log{\left(\tan{\left(x \right)} + 1 \right)} \tan^{2}{\left(x \right)} - \log{\left(\tan{\left(x \right)} + 1 \right)} - \log{\left(\frac{1}{\cos^{2}{\left(x \right)}} \right)} \tan^{2}{\left(x \right)} + \log{\left(\frac{1}{\cos^{2}{\left(x \right)}} \right)}}{4 \left(\tan^{2}{\left(x \right)} - 1\right)}

(-log(1 + tan(x)) - log(-1 + tan(x)) + tan(x)^2*log(1 + tan(x)) + tan(x)^2*log(-1 + tan(x)) - tan(x)^2*log(cos(x)^(-2)) - 4*x*tan(x) + log(cos(x)^(-2)))/(4*(-1 + tan(x)^2))

Respuesta numérica [src]

log(1 + tan(x)^2)/(-4.0 + 4.0*tan(x)^2) - log(1 + tan(x))/(-4.0 + 4.0*tan(x)^2) - log(-1 + tan(x))/(-4.0 + 4.0*tan(x)^2) + tan(x)^2*log(1 + tan(x))/(-4.0 + 4.0*tan(x)^2) + tan(x)^2*log(-1 + tan(x))/(-4.0 + 4.0*tan(x)^2) - tan(x)^2*log(1 + tan(x)^2)/(-4.0 + 4.0*tan(x)^2) - 4.0*x*tan(x)/(-4.0 + 4.0*tan(x)^2)

log(1 + tan(x)^2)/(-4.0 + 4.0*tan(x)^2) - log(1 + tan(x))/(-4.0 + 4.0*tan(x)^2) - log(-1 + tan(x))/(-4.0 + 4.0*tan(x)^2) + tan(x)^2*log(1 + tan(x))/(-4.0 + 4.0*tan(x)^2) + tan(x)^2*log(-1 + tan(x))/(-4.0 + 4.0*tan(x)^2) - tan(x)^2*log(1 + tan(x)^2)/(-4.0 + 4.0*tan(x)^2) - 4.0*x*tan(x)/(-4.0 + 4.0*tan(x)^2)

Denominador racional [src]

                                         2                         2                          2       /       2   \                   /       2   \
-log(1 + tan(x)) - log(-1 + tan(x)) + tan (x)*log(1 + tan(x)) + tan (x)*log(-1 + tan(x)) - tan (x)*log\1 + tan (x)/ - 4*x*tan(x) + log\1 + tan (x)/
---------------------------------------------------------------------------------------------------------------------------------------------------
                                                                             2                                                                     
                                                                   -4 + 4*tan (x)

\frac{- 4 x \tan{\left(x \right)} + \log{\left(\tan{\left(x \right)} - 1 \right)} \tan^{2}{\left(x \right)} - \log{\left(\tan{\left(x \right)} - 1 \right)} + \log{\left(\tan{\left(x \right)} + 1 \right)} \tan^{2}{\left(x \right)} - \log{\left(\tan{\left(x \right)} + 1 \right)} - \log{\left(\tan^{2}{\left(x \right)} + 1 \right)} \tan^{2}{\left(x \right)} + \log{\left(\tan^{2}{\left(x \right)} + 1 \right)}}{4 \tan^{2}{\left(x \right)} - 4}

(-log(1 + tan(x)) - log(-1 + tan(x)) + tan(x)^2*log(1 + tan(x)) + tan(x)^2*log(-1 + tan(x)) - tan(x)^2*log(1 + tan(x)^2) - 4*x*tan(x) + log(1 + tan(x)^2))/(-4 + 4*tan(x)^2)

Unión de expresiones racionales [src]

                                         2                         2                          2       /       2   \                   /       2   \
-log(1 + tan(x)) - log(-1 + tan(x)) + tan (x)*log(1 + tan(x)) + tan (x)*log(-1 + tan(x)) - tan (x)*log\1 + tan (x)/ - 4*x*tan(x) + log\1 + tan (x)/
---------------------------------------------------------------------------------------------------------------------------------------------------
                                                                    /        2   \                                                                 
                                                                  4*\-1 + tan (x)/

\frac{- 4 x \tan{\left(x \right)} + \log{\left(\tan{\left(x \right)} - 1 \right)} \tan^{2}{\left(x \right)} - \log{\left(\tan{\left(x \right)} - 1 \right)} + \log{\left(\tan{\left(x \right)} + 1 \right)} \tan^{2}{\left(x \right)} - \log{\left(\tan{\left(x \right)} + 1 \right)} - \log{\left(\tan^{2}{\left(x \right)} + 1 \right)} \tan^{2}{\left(x \right)} + \log{\left(\tan^{2}{\left(x \right)} + 1 \right)}}{4 \left(\tan^{2}{\left(x \right)} - 1\right)}

(-log(1 + tan(x)) - log(-1 + tan(x)) + tan(x)^2*log(1 + tan(x)) + tan(x)^2*log(-1 + tan(x)) - tan(x)^2*log(1 + tan(x)^2) - 4*x*tan(x) + log(1 + tan(x)^2))/(4*(-1 + tan(x)^2))

Denominador común [src]

     /       2   \                                                    
  log\1 + tan (x)/   log(1 + tan(x))   log(-1 + tan(x))     x*tan(x)  
- ---------------- + --------------- + ---------------- - ------------
         4                  4                 4                   2   
                                                          -1 + tan (x)

- \frac{x \tan{\left(x \right)}}{\tan^{2}{\left(x \right)} - 1} + \frac{\log{\left(\tan{\left(x \right)} - 1 \right)}}{4} + \frac{\log{\left(\tan{\left(x \right)} + 1 \right)}}{4} - \frac{\log{\left(\tan^{2}{\left(x \right)} + 1 \right)}}{4}

-log(1 + tan(x)^2)/4 + log(1 + tan(x))/4 + log(-1 + tan(x))/4 - x*tan(x)/(-1 + tan(x)^2)

Combinatoria [src]

 /     /       2   \      2       /       2   \      2                         2                                                                      \ 
-\- log\1 + tan (x)/ + tan (x)*log\1 + tan (x)/ - tan (x)*log(1 + tan(x)) - tan (x)*log(-1 + tan(x)) + 4*x*tan(x) + log(1 + tan(x)) + log(-1 + tan(x))/ 
--------------------------------------------------------------------------------------------------------------------------------------------------------
                                                              4*(1 + tan(x))*(-1 + tan(x))

- \frac{4 x \tan{\left(x \right)} - \log{\left(\tan{\left(x \right)} - 1 \right)} \tan^{2}{\left(x \right)} + \log{\left(\tan{\left(x \right)} - 1 \right)} - \log{\left(\tan{\left(x \right)} + 1 \right)} \tan^{2}{\left(x \right)} + \log{\left(\tan{\left(x \right)} + 1 \right)} + \log{\left(\tan^{2}{\left(x \right)} + 1 \right)} \tan^{2}{\left(x \right)} - \log{\left(\tan^{2}{\left(x \right)} + 1 \right)}}{4 \left(\tan{\left(x \right)} - 1\right) \left(\tan{\left(x \right)} + 1\right)}

-(-log(1 + tan(x)^2) + tan(x)^2*log(1 + tan(x)^2) - tan(x)^2*log(1 + tan(x)) - tan(x)^2*log(-1 + tan(x)) + 4*x*tan(x) + log(1 + tan(x)) + log(-1 + tan(x)))/(4*(1 + tan(x))*(-1 + tan(x)))

Potencias [src]

   /       2   \                                           2                         2                          2       /       2   \                 
log\1 + tan (x)/   log(1 + tan(x))   log(-1 + tan(x))   tan (x)*log(1 + tan(x))   tan (x)*log(-1 + tan(x))   tan (x)*log\1 + tan (x)/     4*x*tan(x)  
---------------- - --------------- - ---------------- + ----------------------- + ------------------------ - ------------------------ - --------------
           2                  2                 2                      2                         2                          2                     2   
 -4 + 4*tan (x)     -4 + 4*tan (x)    -4 + 4*tan (x)         -4 + 4*tan (x)            -4 + 4*tan (x)             -4 + 4*tan (x)        -4 + 4*tan (x)

- \frac{4 x \tan{\left(x \right)}}{4 \tan^{2}{\left(x \right)} - 4} + \frac{\log{\left(\tan{\left(x \right)} - 1 \right)} \tan^{2}{\left(x \right)}}{4 \tan^{2}{\left(x \right)} - 4} - \frac{\log{\left(\tan{\left(x \right)} - 1 \right)}}{4 \tan^{2}{\left(x \right)} - 4} + \frac{\log{\left(\tan{\left(x \right)} + 1 \right)} \tan^{2}{\left(x \right)}}{4 \tan^{2}{\left(x \right)} - 4} - \frac{\log{\left(\tan{\left(x \right)} + 1 \right)}}{4 \tan^{2}{\left(x \right)} - 4} - \frac{\log{\left(\tan^{2}{\left(x \right)} + 1 \right)} \tan^{2}{\left(x \right)}}{4 \tan^{2}{\left(x \right)} - 4} + \frac{\log{\left(\tan^{2}{\left(x \right)} + 1 \right)}}{4 \tan^{2}{\left(x \right)} - 4}

   /                    2\                                                                                     /                    2\                                                                                                                                             
   |    /   I*x    -I*x\ |                                                                                2    |    /   I*x    -I*x\ |                                                                                                                                             
   |    \- e    + e    / |      /      /   I*x    -I*x\\      /       /   I*x    -I*x\\   /   I*x    -I*x\     |    \- e    + e    / |                   2    /      /   I*x    -I*x\\                   2    /       /   I*x    -I*x\\                                            
log|1 - -----------------|      |    I*\- e    + e    /|      |     I*\- e    + e    /|   \- e    + e    / *log|1 - -----------------|   /   I*x    -I*x\     |    I*\- e    + e    /|   /   I*x    -I*x\     |     I*\- e    + e    /|                                            
   |                   2 |   log|1 + ------------------|   log|-1 + ------------------|                        |                   2 |   \- e    + e    / *log|1 + ------------------|   \- e    + e    / *log|-1 + ------------------|                                            
   |     / I*x    -I*x\  |      |        I*x    -I*x   |      |         I*x    -I*x   |                        |     / I*x    -I*x\  |                        |        I*x    -I*x   |                        |         I*x    -I*x   |                   /   I*x    -I*x\         
   \     \e    + e    /  /      \       e    + e       /      \        e    + e       /                        \     \e    + e    /  /                        \       e    + e       /                        \        e    + e       /             4*I*x*\- e    + e    /         
-------------------------- - --------------------------- - ---------------------------- + -------------------------------------------- - --------------------------------------------- - ---------------------------------------------- - -----------------------------------------
                        2                             2                             2      /                       2\                      /                       2\                      /                       2\                     /                       2\               
        /   I*x    -I*x\              /   I*x    -I*x\              /   I*x    -I*x\       |       /   I*x    -I*x\ |               2      |       /   I*x    -I*x\ |               2      |       /   I*x    -I*x\ |               2     |       /   I*x    -I*x\ |               
      4*\- e    + e    /            4*\- e    + e    /            4*\- e    + e    /       |     4*\- e    + e    / | / I*x    -I*x\       |     4*\- e    + e    / | / I*x    -I*x\       |     4*\- e    + e    / | / I*x    -I*x\      |     4*\- e    + e    / | / I*x    -I*x\
 -4 - -------------------      -4 - -------------------      -4 - -------------------      |-4 - -------------------|*\e    + e    /       |-4 - -------------------|*\e    + e    /       |-4 - -------------------|*\e    + e    /      |-4 - -------------------|*\e    + e    /
                      2                             2                             2        |                     2  |                      |                     2  |                      |                     2  |                     |                     2  |               
        / I*x    -I*x\                / I*x    -I*x\                / I*x    -I*x\         |       / I*x    -I*x\   |                      |       / I*x    -I*x\   |                      |       / I*x    -I*x\   |                     |       / I*x    -I*x\   |               
        \e    + e    /                \e    + e    /                \e    + e    /         \       \e    + e    /   /                      \       \e    + e    /   /                      \       \e    + e    /   /                     \       \e    + e    /   /

- \frac{4 i x \left(- e^{i x} + e^{- i x}\right)}{\left(- \frac{4 \left(- e^{i x} + e^{- i x}\right)^{2}}{\left(e^{i x} + e^{- i x}\right)^{2}} - 4\right) \left(e^{i x} + e^{- i x}\right)} + \frac{\left(- e^{i x} + e^{- i x}\right)^{2} \log{\left(- \frac{\left(- e^{i x} + e^{- i x}\right)^{2}}{\left(e^{i x} + e^{- i x}\right)^{2}} + 1 \right)}}{\left(- \frac{4 \left(- e^{i x} + e^{- i x}\right)^{2}}{\left(e^{i x} + e^{- i x}\right)^{2}} - 4\right) \left(e^{i x} + e^{- i x}\right)^{2}} - \frac{\left(- e^{i x} + e^{- i x}\right)^{2} \log{\left(\frac{i \left(- e^{i x} + e^{- i x}\right)}{e^{i x} + e^{- i x}} - 1 \right)}}{\left(- \frac{4 \left(- e^{i x} + e^{- i x}\right)^{2}}{\left(e^{i x} + e^{- i x}\right)^{2}} - 4\right) \left(e^{i x} + e^{- i x}\right)^{2}} - \frac{\left(- e^{i x} + e^{- i x}\right)^{2} \log{\left(\frac{i \left(- e^{i x} + e^{- i x}\right)}{e^{i x} + e^{- i x}} + 1 \right)}}{\left(- \frac{4 \left(- e^{i x} + e^{- i x}\right)^{2}}{\left(e^{i x} + e^{- i x}\right)^{2}} - 4\right) \left(e^{i x} + e^{- i x}\right)^{2}} + \frac{\log{\left(- \frac{\left(- e^{i x} + e^{- i x}\right)^{2}}{\left(e^{i x} + e^{- i x}\right)^{2}} + 1 \right)}}{- \frac{4 \left(- e^{i x} + e^{- i x}\right)^{2}}{\left(e^{i x} + e^{- i x}\right)^{2}} - 4} - \frac{\log{\left(\frac{i \left(- e^{i x} + e^{- i x}\right)}{e^{i x} + e^{- i x}} - 1 \right)}}{- \frac{4 \left(- e^{i x} + e^{- i x}\right)^{2}}{\left(e^{i x} + e^{- i x}\right)^{2}} - 4} - \frac{\log{\left(\frac{i \left(- e^{i x} + e^{- i x}\right)}{e^{i x} + e^{- i x}} + 1 \right)}}{- \frac{4 \left(- e^{i x} + e^{- i x}\right)^{2}}{\left(e^{i x} + e^{- i x}\right)^{2}} - 4}

log(1 - (-exp(i*x) + exp(-i*x))^2/(exp(i*x) + exp(-i*x))^2)/(-4 - 4*(-exp(i*x) + exp(-i*x))^2/(exp(i*x) + exp(-i*x))^2) - log(1 + i*(-exp(i*x) + exp(-i*x))/(exp(i*x) + exp(-i*x)))/(-4 - 4*(-exp(i*x) + exp(-i*x))^2/(exp(i*x) + exp(-i*x))^2) - log(-1 + i*(-exp(i*x) + exp(-i*x))/(exp(i*x) + exp(-i*x)))/(-4 - 4*(-exp(i*x) + exp(-i*x))^2/(exp(i*x) + exp(-i*x))^2) + (-exp(i*x) + exp(-i*x))^2*log(1 - (-exp(i*x) + exp(-i*x))^2/(exp(i*x) + exp(-i*x))^2)/((-4 - 4*(-exp(i*x) + exp(-i*x))^2/(exp(i*x) + exp(-i*x))^2)*(exp(i*x) + exp(-i*x))^2) - (-exp(i*x) + exp(-i*x))^2*log(1 + i*(-exp(i*x) + exp(-i*x))/(exp(i*x) + exp(-i*x)))/((-4 - 4*(-exp(i*x) + exp(-i*x))^2/(exp(i*x) + exp(-i*x))^2)*(exp(i*x) + exp(-i*x))^2) - (-exp(i*x) + exp(-i*x))^2*log(-1 + i*(-exp(i*x) + exp(-i*x))/(exp(i*x) + exp(-i*x)))/((-4 - 4*(-exp(i*x) + exp(-i*x))^2/(exp(i*x) + exp(-i*x))^2)*(exp(i*x) + exp(-i*x))^2) - 4*i*x*(-exp(i*x) + exp(-i*x))/((-4 - 4*(-exp(i*x) + exp(-i*x))^2/(exp(i*x) + exp(-i*x))^2)*(exp(i*x) + exp(-i*x)))

Compilar la expresión [src]

   /       2   \                                           2                         2                          2       /       2   \                 
log\1 + tan (x)/   log(1 + tan(x))   log(-1 + tan(x))   tan (x)*log(1 + tan(x))   tan (x)*log(-1 + tan(x))   tan (x)*log\1 + tan (x)/     4*x*tan(x)  
---------------- - --------------- - ---------------- + ----------------------- + ------------------------ - ------------------------ - --------------
           2                  2                 2                      2                         2                          2                     2   
 -4 + 4*tan (x)     -4 + 4*tan (x)    -4 + 4*tan (x)         -4 + 4*tan (x)            -4 + 4*tan (x)             -4 + 4*tan (x)        -4 + 4*tan (x)

- \frac{4 x \tan{\left(x \right)}}{4 \tan^{2}{\left(x \right)} - 4} + \frac{\log{\left(\tan{\left(x \right)} - 1 \right)} \tan^{2}{\left(x \right)}}{4 \tan^{2}{\left(x \right)} - 4} - \frac{\log{\left(\tan{\left(x \right)} - 1 \right)}}{4 \tan^{2}{\left(x \right)} - 4} + \frac{\log{\left(\tan{\left(x \right)} + 1 \right)} \tan^{2}{\left(x \right)}}{4 \tan^{2}{\left(x \right)} - 4} - \frac{\log{\left(\tan{\left(x \right)} + 1 \right)}}{4 \tan^{2}{\left(x \right)} - 4} - \frac{\log{\left(\tan^{2}{\left(x \right)} + 1 \right)} \tan^{2}{\left(x \right)}}{4 \tan^{2}{\left(x \right)} - 4} + \frac{\log{\left(\tan^{2}{\left(x \right)} + 1 \right)}}{4 \tan^{2}{\left(x \right)} - 4}

log(1 + tan(x)^2)/(-4 + 4*tan(x)^2) - log(1 + tan(x))/(-4 + 4*tan(x)^2) - log(-1 + tan(x))/(-4 + 4*tan(x)^2) + tan(x)^2*log(1 + tan(x))/(-4 + 4*tan(x)^2) + tan(x)^2*log(-1 + tan(x))/(-4 + 4*tan(x)^2) - tan(x)^2*log(1 + tan(x)^2)/(-4 + 4*tan(x)^2) - 4*x*tan(x)/(-4 + 4*tan(x)^2)

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¿Cómo vas a descomponer esta log(1+tan(x)^2)/(-4+4tan(x)^2)-log(1+tan(x))/(-4+4tan(x)^2)-log(-1+tan(x))/(-4+4tan(x)^2)+tan(x)^2log(1+tan(x))/(-4+4tan(x)^2)+tan(x)^2log(-1+tan(x))/(-4+4tan(x)^2)-tan(x)^2log(1+tan(x)^2)/(-4+4tan(x)^2)-4xtan(x)/(-4+4tan(x)^2) expresión en fracciones?

Solución