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Resolución de integrales/ cos^2/ sin^2/ dx/(sin^2-6*cos^2)

Integral de dx/(sin^2-6*cos^2) dx

Solución

Ha introducido [src]

  1                       
  /                       
 |                        
 |           1            
 |  ------------------- dx
 |     2           2      
 |  sin (x) - 6*cos (x)   
 |                        
/                         
0

$$\int\limits_{0}^{1} \frac{1}{\sin^{2}{\left(x \right)} - 6 \cos^{2}{\left(x \right)}}\, dx$$

Integral(1/(sin(x)^2 - 6*cos(x)^2), (x, 0, 1))

Solución detallada

Vuelva a escribir el integrando:

$\frac{1}{\sin^{2}{\left(x \right)} - 6 \cos^{2}{\left(x \right)}} = - \frac{1}{- \sin^{2}{\left(x \right)} + 6 \cos^{2}{\left(x \right)}}$
La integral del producto de una función por una constante es la constante por la integral de esta función:

$\int \left(- \frac{1}{- \sin^{2}{\left(x \right)} + 6 \cos^{2}{\left(x \right)}}\right)\, dx = - \int \frac{1}{- \sin^{2}{\left(x \right)} + 6 \cos^{2}{\left(x \right)}}\, dx$
1. No puedo encontrar los pasos en la búsqueda de esta integral.
  
  Pero la integral
  
  $- \frac{651 \sqrt{3} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{3} \sqrt{4 - \sqrt{7}}}{3} \right)}}{4620 \sqrt{4 - \sqrt{7}} + 1776 \sqrt{7} \sqrt{4 - \sqrt{7}}} - \frac{237 \sqrt{21} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{3} \sqrt{4 - \sqrt{7}}}{3} \right)}}{4620 \sqrt{4 - \sqrt{7}} + 1776 \sqrt{7} \sqrt{4 - \sqrt{7}}} + \frac{237 \sqrt{21} \log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{\sqrt{3} \sqrt{4 - \sqrt{7}}}{3} \right)}}{4620 \sqrt{4 - \sqrt{7}} + 1776 \sqrt{7} \sqrt{4 - \sqrt{7}}} + \frac{651 \sqrt{3} \log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{\sqrt{3} \sqrt{4 - \sqrt{7}}}{3} \right)}}{4620 \sqrt{4 - \sqrt{7}} + 1776 \sqrt{7} \sqrt{4 - \sqrt{7}}} + \frac{79 \sqrt{21} \sqrt{4 - \sqrt{7}} \sqrt{\sqrt{7} + 4} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{3} \sqrt{\sqrt{7} + 4}}{3} \right)}}{4620 \sqrt{4 - \sqrt{7}} + 1776 \sqrt{7} \sqrt{4 - \sqrt{7}}} + \frac{217 \sqrt{3} \sqrt{4 - \sqrt{7}} \sqrt{\sqrt{7} + 4} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{3} \sqrt{\sqrt{7} + 4}}{3} \right)}}{4620 \sqrt{4 - \sqrt{7}} + 1776 \sqrt{7} \sqrt{4 - \sqrt{7}}} - \frac{217 \sqrt{3} \sqrt{4 - \sqrt{7}} \sqrt{\sqrt{7} + 4} \log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{\sqrt{3} \sqrt{\sqrt{7} + 4}}{3} \right)}}{4620 \sqrt{4 - \sqrt{7}} + 1776 \sqrt{7} \sqrt{4 - \sqrt{7}}} - \frac{79 \sqrt{21} \sqrt{4 - \sqrt{7}} \sqrt{\sqrt{7} + 4} \log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{\sqrt{3} \sqrt{\sqrt{7} + 4}}{3} \right)}}{4620 \sqrt{4 - \sqrt{7}} + 1776 \sqrt{7} \sqrt{4 - \sqrt{7}}}$
Por lo tanto, el resultado es: $\frac{237 \sqrt{21} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{3} \sqrt{4 - \sqrt{7}}}{3} \right)}}{4620 \sqrt{4 - \sqrt{7}} + 1776 \sqrt{7} \sqrt{4 - \sqrt{7}}} + \frac{651 \sqrt{3} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{3} \sqrt{4 - \sqrt{7}}}{3} \right)}}{4620 \sqrt{4 - \sqrt{7}} + 1776 \sqrt{7} \sqrt{4 - \sqrt{7}}} - \frac{651 \sqrt{3} \log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{\sqrt{3} \sqrt{4 - \sqrt{7}}}{3} \right)}}{4620 \sqrt{4 - \sqrt{7}} + 1776 \sqrt{7} \sqrt{4 - \sqrt{7}}} - \frac{237 \sqrt{21} \log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{\sqrt{3} \sqrt{4 - \sqrt{7}}}{3} \right)}}{4620 \sqrt{4 - \sqrt{7}} + 1776 \sqrt{7} \sqrt{4 - \sqrt{7}}} - \frac{217 \sqrt{3} \sqrt{4 - \sqrt{7}} \sqrt{\sqrt{7} + 4} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{3} \sqrt{\sqrt{7} + 4}}{3} \right)}}{4620 \sqrt{4 - \sqrt{7}} + 1776 \sqrt{7} \sqrt{4 - \sqrt{7}}} - \frac{79 \sqrt{21} \sqrt{4 - \sqrt{7}} \sqrt{\sqrt{7} + 4} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{3} \sqrt{\sqrt{7} + 4}}{3} \right)}}{4620 \sqrt{4 - \sqrt{7}} + 1776 \sqrt{7} \sqrt{4 - \sqrt{7}}} + \frac{79 \sqrt{21} \sqrt{4 - \sqrt{7}} \sqrt{\sqrt{7} + 4} \log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{\sqrt{3} \sqrt{\sqrt{7} + 4}}{3} \right)}}{4620 \sqrt{4 - \sqrt{7}} + 1776 \sqrt{7} \sqrt{4 - \sqrt{7}}} + \frac{217 \sqrt{3} \sqrt{4 - \sqrt{7}} \sqrt{\sqrt{7} + 4} \log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{\sqrt{3} \sqrt{\sqrt{7} + 4}}{3} \right)}}{4620 \sqrt{4 - \sqrt{7}} + 1776 \sqrt{7} \sqrt{4 - \sqrt{7}}}$
Ahora simplificar:

$- \frac{- 217 \sqrt{3} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{3} \sqrt{4 - \sqrt{7}}}{3} \right)} - 79 \sqrt{21} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{3} \sqrt{4 - \sqrt{7}}}{3} \right)} + 79 \sqrt{21} \log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{\sqrt{3} \sqrt{4 - \sqrt{7}}}{3} \right)} + 217 \sqrt{3} \log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{\sqrt{3} \sqrt{4 - \sqrt{7}}}{3} \right)} + 79 \sqrt{21} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{3} \sqrt{\sqrt{7} + 4}}{3} \right)} + 217 \sqrt{3} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{3} \sqrt{\sqrt{7} + 4}}{3} \right)} - 217 \sqrt{3} \log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{\sqrt{3} \sqrt{\sqrt{7} + 4}}{3} \right)} - 79 \sqrt{21} \log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{\sqrt{3} \sqrt{\sqrt{7} + 4}}{3} \right)}}{4 \sqrt{4 - \sqrt{7}} \left(385 + 148 \sqrt{7}\right)}$
Añadimos la constante de integración:

$- \frac{- 217 \sqrt{3} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{3} \sqrt{4 - \sqrt{7}}}{3} \right)} - 79 \sqrt{21} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{3} \sqrt{4 - \sqrt{7}}}{3} \right)} + 79 \sqrt{21} \log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{\sqrt{3} \sqrt{4 - \sqrt{7}}}{3} \right)} + 217 \sqrt{3} \log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{\sqrt{3} \sqrt{4 - \sqrt{7}}}{3} \right)} + 79 \sqrt{21} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{3} \sqrt{\sqrt{7} + 4}}{3} \right)} + 217 \sqrt{3} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{3} \sqrt{\sqrt{7} + 4}}{3} \right)} - 217 \sqrt{3} \log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{\sqrt{3} \sqrt{\sqrt{7} + 4}}{3} \right)} - 79 \sqrt{21} \log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{\sqrt{3} \sqrt{\sqrt{7} + 4}}{3} \right)}}{4 \sqrt{4 - \sqrt{7}} \left(385 + 148 \sqrt{7}\right)}+ \mathrm{constant}$

Respuesta:

$- \frac{- 217 \sqrt{3} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{3} \sqrt{4 - \sqrt{7}}}{3} \right)} - 79 \sqrt{21} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{3} \sqrt{4 - \sqrt{7}}}{3} \right)} + 79 \sqrt{21} \log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{\sqrt{3} \sqrt{4 - \sqrt{7}}}{3} \right)} + 217 \sqrt{3} \log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{\sqrt{3} \sqrt{4 - \sqrt{7}}}{3} \right)} + 79 \sqrt{21} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{3} \sqrt{\sqrt{7} + 4}}{3} \right)} + 217 \sqrt{3} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{3} \sqrt{\sqrt{7} + 4}}{3} \right)} - 217 \sqrt{3} \log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{\sqrt{3} \sqrt{\sqrt{7} + 4}}{3} \right)} - 79 \sqrt{21} \log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{\sqrt{3} \sqrt{\sqrt{7} + 4}}{3} \right)}}{4 \sqrt{4 - \sqrt{7}} \left(385 + 148 \sqrt{7}\right)}+ \mathrm{constant}$

Respuesta (Indefinida) [src]

                                               /         ___________         \                   /         ___________         \                  /           ___________         \                 /           ___________         \                                              /           ___________         \                                              /           ___________         \                                              /         ___________         \                                              /         ___________         \
                                               |  ___   /       ___          |                   |  ___   /       ___          |                  |    ___   /       ___          |                 |    ___   /       ___          |                ___________    ___________    |    ___   /       ___          |                ___________    ___________    |    ___   /       ___          |                ___________    ___________    |  ___   /       ___          |                ___________    ___________    |  ___   /       ___          |
  /                                     ___    |\/ 3 *\/  4 - \/ 7        /x\|           ____    |\/ 3 *\/  4 - \/ 7        /x\|          ____    |  \/ 3 *\/  4 - \/ 7        /x\|          ___    |  \/ 3 *\/  4 - \/ 7        /x\|         ___   /       ___    /       ___     |  \/ 3 *\/  4 + \/ 7        /x\|        ____   /       ___    /       ___     |  \/ 3 *\/  4 + \/ 7        /x\|        ____   /       ___    /       ___     |\/ 3 *\/  4 + \/ 7        /x\|         ___   /       ___    /       ___     |\/ 3 *\/  4 + \/ 7        /x\|
 |                                651*\/ 3 *log|-------------------- + tan|-||     237*\/ 21 *log|-------------------- + tan|-||    237*\/ 21 *log|- -------------------- + tan|-||    651*\/ 3 *log|- -------------------- + tan|-||   217*\/ 3 *\/  4 + \/ 7  *\/  4 - \/ 7  *log|- -------------------- + tan|-||   79*\/ 21 *\/  4 + \/ 7  *\/  4 - \/ 7  *log|- -------------------- + tan|-||   79*\/ 21 *\/  4 + \/ 7  *\/  4 - \/ 7  *log|-------------------- + tan|-||   217*\/ 3 *\/  4 + \/ 7  *\/  4 - \/ 7  *log|-------------------- + tan|-||
 |          1                                  \         3                \2//                   \         3                \2//                  \           3                \2//                 \           3                \2//                                              \           3                \2//                                              \           3                \2//                                              \         3                \2//                                              \         3                \2//
 | ------------------- dx = C - ----------------------------------------------- - ----------------------------------------------- + ----------------------------------------------- + ----------------------------------------------- - ---------------------------------------------------------------------------- - ---------------------------------------------------------------------------- + -------------------------------------------------------------------------- + --------------------------------------------------------------------------
 |    2           2                     ___________                 ___________           ___________                 ___________           ___________                 ___________           ___________                 ___________                         ___________                 ___________                                        ___________                 ___________                                       ___________                 ___________                                      ___________                 ___________              
 | sin (x) - 6*cos (x)                 /       ___           ___   /       ___           /       ___           ___   /       ___           /       ___           ___   /       ___           /       ___           ___   /       ___                         /       ___           ___   /       ___                                        /       ___           ___   /       ___                                       /       ___           ___   /       ___                                      /       ___           ___   /       ___               
 |                              4620*\/  4 - \/ 7   + 1776*\/ 7 *\/  4 - \/ 7     4620*\/  4 - \/ 7   + 1776*\/ 7 *\/  4 - \/ 7     4620*\/  4 - \/ 7   + 1776*\/ 7 *\/  4 - \/ 7     4620*\/  4 - \/ 7   + 1776*\/ 7 *\/  4 - \/ 7                   4620*\/  4 - \/ 7   + 1776*\/ 7 *\/  4 - \/ 7                                  4620*\/  4 - \/ 7   + 1776*\/ 7 *\/  4 - \/ 7                                 4620*\/  4 - \/ 7   + 1776*\/ 7 *\/  4 - \/ 7                                4620*\/  4 - \/ 7   + 1776*\/ 7 *\/  4 - \/ 7                
/

$$\int \frac{1}{\sin^{2}{\left(x \right)} - 6 \cos^{2}{\left(x \right)}}\, dx = C + \frac{237 \sqrt{21} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{3} \sqrt{4 - \sqrt{7}}}{3} \right)}}{4620 \sqrt{4 - \sqrt{7}} + 1776 \sqrt{7} \sqrt{4 - \sqrt{7}}} + \frac{651 \sqrt{3} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{3} \sqrt{4 - \sqrt{7}}}{3} \right)}}{4620 \sqrt{4 - \sqrt{7}} + 1776 \sqrt{7} \sqrt{4 - \sqrt{7}}} - \frac{651 \sqrt{3} \log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{\sqrt{3} \sqrt{4 - \sqrt{7}}}{3} \right)}}{4620 \sqrt{4 - \sqrt{7}} + 1776 \sqrt{7} \sqrt{4 - \sqrt{7}}} - \frac{237 \sqrt{21} \log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{\sqrt{3} \sqrt{4 - \sqrt{7}}}{3} \right)}}{4620 \sqrt{4 - \sqrt{7}} + 1776 \sqrt{7} \sqrt{4 - \sqrt{7}}} - \frac{217 \sqrt{3} \sqrt{4 - \sqrt{7}} \sqrt{\sqrt{7} + 4} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{3} \sqrt{\sqrt{7} + 4}}{3} \right)}}{4620 \sqrt{4 - \sqrt{7}} + 1776 \sqrt{7} \sqrt{4 - \sqrt{7}}} - \frac{79 \sqrt{21} \sqrt{4 - \sqrt{7}} \sqrt{\sqrt{7} + 4} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{3} \sqrt{\sqrt{7} + 4}}{3} \right)}}{4620 \sqrt{4 - \sqrt{7}} + 1776 \sqrt{7} \sqrt{4 - \sqrt{7}}} + \frac{79 \sqrt{21} \sqrt{4 - \sqrt{7}} \sqrt{\sqrt{7} + 4} \log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{\sqrt{3} \sqrt{\sqrt{7} + 4}}{3} \right)}}{4620 \sqrt{4 - \sqrt{7}} + 1776 \sqrt{7} \sqrt{4 - \sqrt{7}}} + \frac{217 \sqrt{3} \sqrt{4 - \sqrt{7}} \sqrt{\sqrt{7} + 4} \log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{\sqrt{3} \sqrt{\sqrt{7} + 4}}{3} \right)}}{4620 \sqrt{4 - \sqrt{7}} + 1776 \sqrt{7} \sqrt{4 - \sqrt{7}}}$$

Simplificar

Gráfica

Trazar el gráfico f(x)

Respuesta [src]

              /          /         ___________\\                  /         ___________           \               /          /         ___________\\                  /         ___________           \              /          /                     ___________\\                       /         ___________\                  /          /                     ___________\\                      /         ___________\                                                 /          /                     ___________\\                                              /         ___________\                                           /          /                     ___________\\                                              /         ___________\                                           /          /         ___________\\                                              /         ___________           \                                           /          /         ___________\\                                              /         ___________           \
              |          |  ___   /       ___ ||                  |  ___   /       ___            |               |          |  ___   /       ___ ||                  |  ___   /       ___            |              |          |              ___   /       ___ ||                       |  ___   /       ___ |                  |          |              ___   /       ___ ||                      |  ___   /       ___ |                      ___________    ___________ |          |              ___   /       ___ ||                ___________    ___________    |  ___   /       ___ |                ___________    ___________ |          |              ___   /       ___ ||                ___________    ___________    |  ___   /       ___ |                ___________    ___________ |          |  ___   /       ___ ||                ___________    ___________    |  ___   /       ___            |                ___________    ___________ |          |  ___   /       ___ ||                ___________    ___________    |  ___   /       ___            |
          ___ |          |\/ 3 *\/  4 - \/ 7  ||           ___    |\/ 3 *\/  4 - \/ 7             |          ____ |          |\/ 3 *\/  4 - \/ 7  ||          ____    |\/ 3 *\/  4 - \/ 7             |         ____ |          |            \/ 3 *\/  4 - \/ 7  ||               ____    |\/ 3 *\/  4 - \/ 7  |              ___ |          |            \/ 3 *\/  4 - \/ 7  ||               ___    |\/ 3 *\/  4 - \/ 7  |               ___   /       ___    /       ___  |          |            \/ 3 *\/  4 + \/ 7  ||         ___   /       ___    /       ___     |\/ 3 *\/  4 + \/ 7  |        ____   /       ___    /       ___  |          |            \/ 3 *\/  4 + \/ 7  ||        ____   /       ___    /       ___     |\/ 3 *\/  4 + \/ 7  |        ____   /       ___    /       ___  |          |\/ 3 *\/  4 + \/ 7  ||        ____   /       ___    /       ___     |\/ 3 *\/  4 + \/ 7             |         ___   /       ___    /       ___  |          |\/ 3 *\/  4 + \/ 7  ||         ___   /       ___    /       ___     |\/ 3 *\/  4 + \/ 7             |
    651*\/ 3 *|pi*I + log|--------------------||     651*\/ 3 *log|-------------------- + tan(1/2)|    237*\/ 21 *|pi*I + log|--------------------||    237*\/ 21 *log|-------------------- + tan(1/2)|   237*\/ 21 *|pi*I + log|-tan(1/2) + --------------------||         237*\/ 21 *log|--------------------|        651*\/ 3 *|pi*I + log|-tan(1/2) + --------------------||         651*\/ 3 *log|--------------------|         217*\/ 3 *\/  4 + \/ 7  *\/  4 - \/ 7  *|pi*I + log|-tan(1/2) + --------------------||   217*\/ 3 *\/  4 + \/ 7  *\/  4 - \/ 7  *log|--------------------|   79*\/ 21 *\/  4 + \/ 7  *\/  4 - \/ 7  *|pi*I + log|-tan(1/2) + --------------------||   79*\/ 21 *\/  4 + \/ 7  *\/  4 - \/ 7  *log|--------------------|   79*\/ 21 *\/  4 + \/ 7  *\/  4 - \/ 7  *|pi*I + log|--------------------||   79*\/ 21 *\/  4 + \/ 7  *\/  4 - \/ 7  *log|-------------------- + tan(1/2)|   217*\/ 3 *\/  4 + \/ 7  *\/  4 - \/ 7  *|pi*I + log|--------------------||   217*\/ 3 *\/  4 + \/ 7  *\/  4 - \/ 7  *log|-------------------- + tan(1/2)|
              \          \         3          //                  \         3                     /               \          \         3          //                  \         3                     /              \          \                     3          //                       \         3          /                  \          \                     3          //                      \         3          /                                                 \          \                     3          //                                              \         3          /                                           \          \                     3          //                                              \         3          /                                           \          \         3          //                                              \         3                     /                                           \          \         3          //                                              \         3                     /
- ----------------------------------------------- - ----------------------------------------------- - ----------------------------------------------- - ----------------------------------------------- + --------------------------------------------------------- + ----------------------------------------------- + -------------------------------------------------------- + ----------------------------------------------- - -------------------------------------------------------------------------------------- - ----------------------------------------------------------------- - -------------------------------------------------------------------------------------- - ----------------------------------------------------------------- + -------------------------------------------------------------------------- + ---------------------------------------------------------------------------- + -------------------------------------------------------------------------- + ----------------------------------------------------------------------------
          ___________                 ___________           ___________                 ___________           ___________                 ___________           ___________                 ___________                ___________                 ___________                ___________                 ___________               ___________                 ___________                ___________                 ___________                              ___________                 ___________                                        ___________                 ___________                                       ___________                 ___________                                        ___________                 ___________                                 ___________                 ___________                                       ___________                 ___________                                       ___________                 ___________                                       ___________                 ___________               
         /       ___           ___   /       ___           /       ___           ___   /       ___           /       ___           ___   /       ___           /       ___           ___   /       ___                /       ___           ___   /       ___                /       ___           ___   /       ___               /       ___           ___   /       ___                /       ___           ___   /       ___                              /       ___           ___   /       ___                                        /       ___           ___   /       ___                                       /       ___           ___   /       ___                                        /       ___           ___   /       ___                                 /       ___           ___   /       ___                                       /       ___           ___   /       ___                                       /       ___           ___   /       ___                                       /       ___           ___   /       ___                
  4620*\/  4 - \/ 7   + 1776*\/ 7 *\/  4 - \/ 7     4620*\/  4 - \/ 7   + 1776*\/ 7 *\/  4 - \/ 7     4620*\/  4 - \/ 7   + 1776*\/ 7 *\/  4 - \/ 7     4620*\/  4 - \/ 7   + 1776*\/ 7 *\/  4 - \/ 7          4620*\/  4 - \/ 7   + 1776*\/ 7 *\/  4 - \/ 7          4620*\/  4 - \/ 7   + 1776*\/ 7 *\/  4 - \/ 7         4620*\/  4 - \/ 7   + 1776*\/ 7 *\/  4 - \/ 7          4620*\/  4 - \/ 7   + 1776*\/ 7 *\/  4 - \/ 7                        4620*\/  4 - \/ 7   + 1776*\/ 7 *\/  4 - \/ 7                                  4620*\/  4 - \/ 7   + 1776*\/ 7 *\/  4 - \/ 7                                 4620*\/  4 - \/ 7   + 1776*\/ 7 *\/  4 - \/ 7                                  4620*\/  4 - \/ 7   + 1776*\/ 7 *\/  4 - \/ 7                           4620*\/  4 - \/ 7   + 1776*\/ 7 *\/  4 - \/ 7                                 4620*\/  4 - \/ 7   + 1776*\/ 7 *\/  4 - \/ 7                                 4620*\/  4 - \/ 7   + 1776*\/ 7 *\/  4 - \/ 7                                 4620*\/  4 - \/ 7   + 1776*\/ 7 *\/  4 - \/ 7

$$- \frac{217 \sqrt{3} \sqrt{4 - \sqrt{7}} \sqrt{\sqrt{7} + 4} \log{\left(\frac{\sqrt{3} \sqrt{\sqrt{7} + 4}}{3} \right)}}{4620 \sqrt{4 - \sqrt{7}} + 1776 \sqrt{7} \sqrt{4 - \sqrt{7}}} + \frac{651 \sqrt{3} \log{\left(\frac{\sqrt{3} \sqrt{4 - \sqrt{7}}}{3} \right)}}{4620 \sqrt{4 - \sqrt{7}} + 1776 \sqrt{7} \sqrt{4 - \sqrt{7}}} + \frac{237 \sqrt{21} \log{\left(\frac{\sqrt{3} \sqrt{4 - \sqrt{7}}}{3} \right)}}{4620 \sqrt{4 - \sqrt{7}} + 1776 \sqrt{7} \sqrt{4 - \sqrt{7}}} - \frac{79 \sqrt{21} \sqrt{4 - \sqrt{7}} \sqrt{\sqrt{7} + 4} \log{\left(\frac{\sqrt{3} \sqrt{\sqrt{7} + 4}}{3} \right)}}{4620 \sqrt{4 - \sqrt{7}} + 1776 \sqrt{7} \sqrt{4 - \sqrt{7}}} - \frac{651 \sqrt{3} \log{\left(\tan{\left(\frac{1}{2} \right)} + \frac{\sqrt{3} \sqrt{4 - \sqrt{7}}}{3} \right)}}{4620 \sqrt{4 - \sqrt{7}} + 1776 \sqrt{7} \sqrt{4 - \sqrt{7}}} - \frac{237 \sqrt{21} \log{\left(\tan{\left(\frac{1}{2} \right)} + \frac{\sqrt{3} \sqrt{4 - \sqrt{7}}}{3} \right)}}{4620 \sqrt{4 - \sqrt{7}} + 1776 \sqrt{7} \sqrt{4 - \sqrt{7}}} + \frac{79 \sqrt{21} \sqrt{4 - \sqrt{7}} \sqrt{\sqrt{7} + 4} \log{\left(\tan{\left(\frac{1}{2} \right)} + \frac{\sqrt{3} \sqrt{\sqrt{7} + 4}}{3} \right)}}{4620 \sqrt{4 - \sqrt{7}} + 1776 \sqrt{7} \sqrt{4 - \sqrt{7}}} + \frac{217 \sqrt{3} \sqrt{4 - \sqrt{7}} \sqrt{\sqrt{7} + 4} \log{\left(\tan{\left(\frac{1}{2} \right)} + \frac{\sqrt{3} \sqrt{\sqrt{7} + 4}}{3} \right)}}{4620 \sqrt{4 - \sqrt{7}} + 1776 \sqrt{7} \sqrt{4 - \sqrt{7}}} - \frac{217 \sqrt{3} \sqrt{4 - \sqrt{7}} \sqrt{\sqrt{7} + 4} \left(\log{\left(- \tan{\left(\frac{1}{2} \right)} + \frac{\sqrt{3} \sqrt{\sqrt{7} + 4}}{3} \right)} + i \pi\right)}{4620 \sqrt{4 - \sqrt{7}} + 1776 \sqrt{7} \sqrt{4 - \sqrt{7}}} - \frac{651 \sqrt{3} \left(\log{\left(\frac{\sqrt{3} \sqrt{4 - \sqrt{7}}}{3} \right)} + i \pi\right)}{4620 \sqrt{4 - \sqrt{7}} + 1776 \sqrt{7} \sqrt{4 - \sqrt{7}}} - \frac{79 \sqrt{21} \sqrt{4 - \sqrt{7}} \sqrt{\sqrt{7} + 4} \left(\log{\left(- \tan{\left(\frac{1}{2} \right)} + \frac{\sqrt{3} \sqrt{\sqrt{7} + 4}}{3} \right)} + i \pi\right)}{4620 \sqrt{4 - \sqrt{7}} + 1776 \sqrt{7} \sqrt{4 - \sqrt{7}}} - \frac{237 \sqrt{21} \left(\log{\left(\frac{\sqrt{3} \sqrt{4 - \sqrt{7}}}{3} \right)} + i \pi\right)}{4620 \sqrt{4 - \sqrt{7}} + 1776 \sqrt{7} \sqrt{4 - \sqrt{7}}} + \frac{237 \sqrt{21} \left(\log{\left(- \tan{\left(\frac{1}{2} \right)} + \frac{\sqrt{3} \sqrt{4 - \sqrt{7}}}{3} \right)} + i \pi\right)}{4620 \sqrt{4 - \sqrt{7}} + 1776 \sqrt{7} \sqrt{4 - \sqrt{7}}} + \frac{79 \sqrt{21} \sqrt{4 - \sqrt{7}} \sqrt{\sqrt{7} + 4} \left(\log{\left(\frac{\sqrt{3} \sqrt{\sqrt{7} + 4}}{3} \right)} + i \pi\right)}{4620 \sqrt{4 - \sqrt{7}} + 1776 \sqrt{7} \sqrt{4 - \sqrt{7}}} + \frac{651 \sqrt{3} \left(\log{\left(- \tan{\left(\frac{1}{2} \right)} + \frac{\sqrt{3} \sqrt{4 - \sqrt{7}}}{3} \right)} + i \pi\right)}{4620 \sqrt{4 - \sqrt{7}} + 1776 \sqrt{7} \sqrt{4 - \sqrt{7}}} + \frac{217 \sqrt{3} \sqrt{4 - \sqrt{7}} \sqrt{\sqrt{7} + 4} \left(\log{\left(\frac{\sqrt{3} \sqrt{\sqrt{7} + 4}}{3} \right)} + i \pi\right)}{4620 \sqrt{4 - \sqrt{7}} + 1776 \sqrt{7} \sqrt{4 - \sqrt{7}}}$$

              /          /         ___________\\                  /         ___________           \               /          /         ___________\\                  /         ___________           \              /          /                     ___________\\                       /         ___________\                  /          /                     ___________\\                      /         ___________\                                                 /          /                     ___________\\                                              /         ___________\                                           /          /                     ___________\\                                              /         ___________\                                           /          /         ___________\\                                              /         ___________           \                                           /          /         ___________\\                                              /         ___________           \
              |          |  ___   /       ___ ||                  |  ___   /       ___            |               |          |  ___   /       ___ ||                  |  ___   /       ___            |              |          |              ___   /       ___ ||                       |  ___   /       ___ |                  |          |              ___   /       ___ ||                      |  ___   /       ___ |                      ___________    ___________ |          |              ___   /       ___ ||                ___________    ___________    |  ___   /       ___ |                ___________    ___________ |          |              ___   /       ___ ||                ___________    ___________    |  ___   /       ___ |                ___________    ___________ |          |  ___   /       ___ ||                ___________    ___________    |  ___   /       ___            |                ___________    ___________ |          |  ___   /       ___ ||                ___________    ___________    |  ___   /       ___            |
          ___ |          |\/ 3 *\/  4 - \/ 7  ||           ___    |\/ 3 *\/  4 - \/ 7             |          ____ |          |\/ 3 *\/  4 - \/ 7  ||          ____    |\/ 3 *\/  4 - \/ 7             |         ____ |          |            \/ 3 *\/  4 - \/ 7  ||               ____    |\/ 3 *\/  4 - \/ 7  |              ___ |          |            \/ 3 *\/  4 - \/ 7  ||               ___    |\/ 3 *\/  4 - \/ 7  |               ___   /       ___    /       ___  |          |            \/ 3 *\/  4 + \/ 7  ||         ___   /       ___    /       ___     |\/ 3 *\/  4 + \/ 7  |        ____   /       ___    /       ___  |          |            \/ 3 *\/  4 + \/ 7  ||        ____   /       ___    /       ___     |\/ 3 *\/  4 + \/ 7  |        ____   /       ___    /       ___  |          |\/ 3 *\/  4 + \/ 7  ||        ____   /       ___    /       ___     |\/ 3 *\/  4 + \/ 7             |         ___   /       ___    /       ___  |          |\/ 3 *\/  4 + \/ 7  ||         ___   /       ___    /       ___     |\/ 3 *\/  4 + \/ 7             |
    651*\/ 3 *|pi*I + log|--------------------||     651*\/ 3 *log|-------------------- + tan(1/2)|    237*\/ 21 *|pi*I + log|--------------------||    237*\/ 21 *log|-------------------- + tan(1/2)|   237*\/ 21 *|pi*I + log|-tan(1/2) + --------------------||         237*\/ 21 *log|--------------------|        651*\/ 3 *|pi*I + log|-tan(1/2) + --------------------||         651*\/ 3 *log|--------------------|         217*\/ 3 *\/  4 + \/ 7  *\/  4 - \/ 7  *|pi*I + log|-tan(1/2) + --------------------||   217*\/ 3 *\/  4 + \/ 7  *\/  4 - \/ 7  *log|--------------------|   79*\/ 21 *\/  4 + \/ 7  *\/  4 - \/ 7  *|pi*I + log|-tan(1/2) + --------------------||   79*\/ 21 *\/  4 + \/ 7  *\/  4 - \/ 7  *log|--------------------|   79*\/ 21 *\/  4 + \/ 7  *\/  4 - \/ 7  *|pi*I + log|--------------------||   79*\/ 21 *\/  4 + \/ 7  *\/  4 - \/ 7  *log|-------------------- + tan(1/2)|   217*\/ 3 *\/  4 + \/ 7  *\/  4 - \/ 7  *|pi*I + log|--------------------||   217*\/ 3 *\/  4 + \/ 7  *\/  4 - \/ 7  *log|-------------------- + tan(1/2)|
              \          \         3          //                  \         3                     /               \          \         3          //                  \         3                     /              \          \                     3          //                       \         3          /                  \          \                     3          //                      \         3          /                                                 \          \                     3          //                                              \         3          /                                           \          \                     3          //                                              \         3          /                                           \          \         3          //                                              \         3                     /                                           \          \         3          //                                              \         3                     /
- ----------------------------------------------- - ----------------------------------------------- - ----------------------------------------------- - ----------------------------------------------- + --------------------------------------------------------- + ----------------------------------------------- + -------------------------------------------------------- + ----------------------------------------------- - -------------------------------------------------------------------------------------- - ----------------------------------------------------------------- - -------------------------------------------------------------------------------------- - ----------------------------------------------------------------- + -------------------------------------------------------------------------- + ---------------------------------------------------------------------------- + -------------------------------------------------------------------------- + ----------------------------------------------------------------------------
          ___________                 ___________           ___________                 ___________           ___________                 ___________           ___________                 ___________                ___________                 ___________                ___________                 ___________               ___________                 ___________                ___________                 ___________                              ___________                 ___________                                        ___________                 ___________                                       ___________                 ___________                                        ___________                 ___________                                 ___________                 ___________                                       ___________                 ___________                                       ___________                 ___________                                       ___________                 ___________               
         /       ___           ___   /       ___           /       ___           ___   /       ___           /       ___           ___   /       ___           /       ___           ___   /       ___                /       ___           ___   /       ___                /       ___           ___   /       ___               /       ___           ___   /       ___                /       ___           ___   /       ___                              /       ___           ___   /       ___                                        /       ___           ___   /       ___                                       /       ___           ___   /       ___                                        /       ___           ___   /       ___                                 /       ___           ___   /       ___                                       /       ___           ___   /       ___                                       /       ___           ___   /       ___                                       /       ___           ___   /       ___                
  4620*\/  4 - \/ 7   + 1776*\/ 7 *\/  4 - \/ 7     4620*\/  4 - \/ 7   + 1776*\/ 7 *\/  4 - \/ 7     4620*\/  4 - \/ 7   + 1776*\/ 7 *\/  4 - \/ 7     4620*\/  4 - \/ 7   + 1776*\/ 7 *\/  4 - \/ 7          4620*\/  4 - \/ 7   + 1776*\/ 7 *\/  4 - \/ 7          4620*\/  4 - \/ 7   + 1776*\/ 7 *\/  4 - \/ 7         4620*\/  4 - \/ 7   + 1776*\/ 7 *\/  4 - \/ 7          4620*\/  4 - \/ 7   + 1776*\/ 7 *\/  4 - \/ 7                        4620*\/  4 - \/ 7   + 1776*\/ 7 *\/  4 - \/ 7                                  4620*\/  4 - \/ 7   + 1776*\/ 7 *\/  4 - \/ 7                                 4620*\/  4 - \/ 7   + 1776*\/ 7 *\/  4 - \/ 7                                  4620*\/  4 - \/ 7   + 1776*\/ 7 *\/  4 - \/ 7                           4620*\/  4 - \/ 7   + 1776*\/ 7 *\/  4 - \/ 7                                 4620*\/  4 - \/ 7   + 1776*\/ 7 *\/  4 - \/ 7                                 4620*\/  4 - \/ 7   + 1776*\/ 7 *\/  4 - \/ 7                                 4620*\/  4 - \/ 7   + 1776*\/ 7 *\/  4 - \/ 7

-651*sqrt(3)*(pi*i + log(sqrt(3)*sqrt(4 - sqrt(7))/3))/(4620*sqrt(4 - sqrt(7)) + 1776*sqrt(7)*sqrt(4 - sqrt(7))) - 651*sqrt(3)*log(sqrt(3)*sqrt(4 - sqrt(7))/3 + tan(1/2))/(4620*sqrt(4 - sqrt(7)) + 1776*sqrt(7)*sqrt(4 - sqrt(7))) - 237*sqrt(21)*(pi*i + log(sqrt(3)*sqrt(4 - sqrt(7))/3))/(4620*sqrt(4 - sqrt(7)) + 1776*sqrt(7)*sqrt(4 - sqrt(7))) - 237*sqrt(21)*log(sqrt(3)*sqrt(4 - sqrt(7))/3 + tan(1/2))/(4620*sqrt(4 - sqrt(7)) + 1776*sqrt(7)*sqrt(4 - sqrt(7))) + 237*sqrt(21)*(pi*i + log(-tan(1/2) + sqrt(3)*sqrt(4 - sqrt(7))/3))/(4620*sqrt(4 - sqrt(7)) + 1776*sqrt(7)*sqrt(4 - sqrt(7))) + 237*sqrt(21)*log(sqrt(3)*sqrt(4 - sqrt(7))/3)/(4620*sqrt(4 - sqrt(7)) + 1776*sqrt(7)*sqrt(4 - sqrt(7))) + 651*sqrt(3)*(pi*i + log(-tan(1/2) + sqrt(3)*sqrt(4 - sqrt(7))/3))/(4620*sqrt(4 - sqrt(7)) + 1776*sqrt(7)*sqrt(4 - sqrt(7))) + 651*sqrt(3)*log(sqrt(3)*sqrt(4 - sqrt(7))/3)/(4620*sqrt(4 - sqrt(7)) + 1776*sqrt(7)*sqrt(4 - sqrt(7))) - 217*sqrt(3)*sqrt(4 + sqrt(7))*sqrt(4 - sqrt(7))*(pi*i + log(-tan(1/2) + sqrt(3)*sqrt(4 + sqrt(7))/3))/(4620*sqrt(4 - sqrt(7)) + 1776*sqrt(7)*sqrt(4 - sqrt(7))) - 217*sqrt(3)*sqrt(4 + sqrt(7))*sqrt(4 - sqrt(7))*log(sqrt(3)*sqrt(4 + sqrt(7))/3)/(4620*sqrt(4 - sqrt(7)) + 1776*sqrt(7)*sqrt(4 - sqrt(7))) - 79*sqrt(21)*sqrt(4 + sqrt(7))*sqrt(4 - sqrt(7))*(pi*i + log(-tan(1/2) + sqrt(3)*sqrt(4 + sqrt(7))/3))/(4620*sqrt(4 - sqrt(7)) + 1776*sqrt(7)*sqrt(4 - sqrt(7))) - 79*sqrt(21)*sqrt(4 + sqrt(7))*sqrt(4 - sqrt(7))*log(sqrt(3)*sqrt(4 + sqrt(7))/3)/(4620*sqrt(4 - sqrt(7)) + 1776*sqrt(7)*sqrt(4 - sqrt(7))) + 79*sqrt(21)*sqrt(4 + sqrt(7))*sqrt(4 - sqrt(7))*(pi*i + log(sqrt(3)*sqrt(4 + sqrt(7))/3))/(4620*sqrt(4 - sqrt(7)) + 1776*sqrt(7)*sqrt(4 - sqrt(7))) + 79*sqrt(21)*sqrt(4 + sqrt(7))*sqrt(4 - sqrt(7))*log(sqrt(3)*sqrt(4 + sqrt(7))/3 + tan(1/2))/(4620*sqrt(4 - sqrt(7)) + 1776*sqrt(7)*sqrt(4 - sqrt(7))) + 217*sqrt(3)*sqrt(4 + sqrt(7))*sqrt(4 - sqrt(7))*(pi*i + log(sqrt(3)*sqrt(4 + sqrt(7))/3))/(4620*sqrt(4 - sqrt(7)) + 1776*sqrt(7)*sqrt(4 - sqrt(7))) + 217*sqrt(3)*sqrt(4 + sqrt(7))*sqrt(4 - sqrt(7))*log(sqrt(3)*sqrt(4 + sqrt(7))/3 + tan(1/2))/(4620*sqrt(4 - sqrt(7)) + 1776*sqrt(7)*sqrt(4 - sqrt(7)))

Respuesta numérica [src]

-0.306638239544892

-0.306638239544892

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