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Resolución de integrales/ x^5+1/ 1/(x^5+1)

Integral de 1/(x^5+1) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1          
  /          
 |           
 |    1      
 |  ------ dx
 |   5       
 |  x  + 1   
 |           
/            
0
$$\int\limits_{0}^{1} \frac{1}{x^{5} + 1}\, dx$$ 
Integral(1/(x^5 + 1), (x, 0, 1))
Solución detallada

  1. Vuelva a escribir el integrando:

  2. Integramos término a término:

    1. La integral del producto de una función por una constante es la constante por la integral de esta función:

      1. Vuelva a escribir el integrando:

      2. Integramos término a término:

        1. No puedo encontrar los pasos en la búsqueda de esta integral.

          Pero la integral

        1. La integral del producto de una función por una constante es la constante por la integral de esta función:

          1. No puedo encontrar los pasos en la búsqueda de esta integral.

            Pero la integral

          Por lo tanto, el resultado es:

        1. La integral del producto de una función por una constante es la constante por la integral de esta función:

          1. No puedo encontrar los pasos en la búsqueda de esta integral.

            Pero la integral

          Por lo tanto, el resultado es:

        1. La integral del producto de una función por una constante es la constante por la integral de esta función:

          1. No puedo encontrar los pasos en la búsqueda de esta integral.

            Pero la integral

          Por lo tanto, el resultado es:

        El resultado es:

      Por lo tanto, el resultado es:

    1. La integral del producto de una función por una constante es la constante por la integral de esta función:

      1. que .

        Luego que y ponemos :

        1. Integral es .

        Si ahora sustituir más en:

      Por lo tanto, el resultado es:

    El resultado es:

  3. Ahora simplificar:

  4. Añadimos la constante de integración:

Respuesta:

Respuesta (Indefinida) [src] 
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ____________________________                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ____________________________                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ____________________________                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   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                                     /   1    \/ 10 *\/  3 + \/ 5        |                                                                     18                                                                                                                                            32*x                                                                                                                                         22*\/ 5                                                                                                                                 \/ 10 *\/  3 + \/ 5                                                                                                                           15*\/ 2 *\/  3 + \/ 5                                                             |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               /   1    \/ 10 *\/  3 - \/ 5        |                                                                     18                                                                                                                                            32*x                                                                                                                                         22*\/ 5                                                                                                                                 \/ 10 *\/  3 - \/ 5                                                                                                                           15*\/ 2 *\/  3 - \/ 5                                                             |                                                                                                                                                                                 /   3    \/ 10 *\/  3 + \/ 5        |                                                                      94                                                                                                                                              44*x                                                                                                                                           92*\/ 5                                                                                                                                  75*\/ 2 *\/  3 + \/ 5                                                                                                                            6*\/ 10 *\/  3 + \/ 5                                                              |        /   3    \/ 10 *\/  3 - \/ 5        |                                                                      94                                                                                                                                            92*\/ 5                                                                                                                                            44*x                                                                                                                                   6*\/ 10 *\/  3 - \/ 5                                                                                                                            75*\/ 2 *\/  3 - \/ 5                                                              |         /        ___      /                  ____                                    ___                                       ___              \         /        ___      /                   ___                                       ____                                        ___               \        /   3    \/ 10 *\/  3 + \/ 5        |                                                                         96                                                                                                                                             42*\/ 5                                                                                                                                             44*x                                                                                                                                    8*\/ 10 *\/  3 + \/ 5                                                                                                                             45*\/ 2 *\/  3 + \/ 5                                                              |        /   3    \/ 10 *\/  3 - \/ 5        |                                                                         96                                                                                                                                             42*\/ 5                                                                                                                                             44*x                                                                                                                                    45*\/ 2 *\/  3 - \/ 5                                                                                                                             8*\/ 10 *\/  3 - \/ 5                                                              |
                                2*  /    -- - --------------------- *atan|-------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------|              /                           /                              ___________               ___________\                  ___________                 ___________\                  /                      /                             ___________             ___________\                ___________               ___________\                  /                      /                           ___________               ___________\                ___________               ___________\            /                            /                            ___________               ___________\                 ___________                  ___________\            /                            /                            ___________               ___________\                  ___________                 ___________\   2*  /    -- - --------------------- *atan|-------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------|              /                           /                              ___________               ___________\                 ___________                  ___________\   4*  /    -- - --------------------- *atan|---------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------- - 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--------------------- *atan|- ----------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------|   8*  /    -- - --------------------- *atan|- ----------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------- - 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                                  \/     20            200               |           ____________________________               ____________________________                              ____________________________              ____________________________               ____________________________                              ____________________________              ____________________________               ____________________________                              ____________________________              ____________________________               ____________________________                              ____________________________              ____________________________               ____________________________                              ____________________________|              |                   ___     |            ___        ___   /       ___        ____   /       ___ |          ____   /       ___           ___   /       ___ |   /      ___\    |              ___     |           ___        ___   /       ___      ____   /       ___ |        ____   /       ___         ___   /       ___ |   /      ___\    |              ___     |           ___     ____   /       ___         ___   /       ___ |        ____   /       ___         ___   /       ___ |            |                    ___     |          ___        ___   /       ___        ____   /       ___ |          ___   /       ___           ____   /       ___ |            |                    ___     |          ___       ____   /       ___         ___   /       ___ |          ____   /       ___           ___   /       ___ |     \/     20            200               |           ____________________________               ____________________________                              ____________________________              ____________________________               ____________________________                              ____________________________              ____________________________               ____________________________                              ____________________________              ____________________________               ____________________________                              ____________________________              ____________________________               ____________________________                              ____________________________|              |                   ___     |            ___       ____   /       ___         ___   /       ___ |          ___   /       ___           ____   /       ___ |     \/     20             50               |      ______________________________               ______________________________                               ______________________________         ______________________________               ______________________________                               ______________________________         ______________________________               ______________________________                               ______________________________         ______________________________               ______________________________                               ______________________________         ______________________________               ______________________________                               ______________________________|     \/     20             50               |      ______________________________               ______________________________                               ______________________________         ______________________________               ______________________________                               ______________________________         ______________________________               ______________________________                               ______________________________         ______________________________               ______________________________                               ______________________________         ______________________________               ______________________________                               ______________________________|   6*  /   -- - ----- *atan|------------------------------------- - ------------------------------------- + -------------------------------------|   6*  /   -- + ----- *atan|--------------------------------------- + --------------------------------------- - ---------------------------------------|     \/     20             50               |         ______________________________               ______________________________                               ______________________________          ______________________________               ______________________________                               ______________________________          ______________________________               ______________________________                               ______________________________          ______________________________               ______________________________                               ______________________________          ______________________________               ______________________________                               ______________________________|     \/     20             50               |         ______________________________               ______________________________                               ______________________________          ______________________________               ______________________________                               ______________________________          ______________________________               ______________________________                               ______________________________          ______________________________               ______________________________                               ______________________________          ______________________________               ______________________________                               ______________________________|
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\/ 5     \/ 10 *\/  3 - \/ 5  |   37*\/ 10 *\/  3 - \/ 5     35*\/ 2 *\/  3 - \/ 5  |   |1   \/ 5 |    |71    2   9*\/ 5      |  9   11*\/ 5    \/ 10 *\/  3 + \/ 5     15*\/ 2 *\/  3 + \/ 5  |   37*\/ 10 *\/  3 + \/ 5     35*\/ 2 *\/  3 + \/ 5  |     ___    |12387    2   4287*\/ 5      |47   46*\/ 5    75*\/ 2 *\/  3 + \/ 5     3*\/ 10 *\/  3 + \/ 5  |   4645*\/ 2 *\/  3 + \/ 5     3929*\/ 10 *\/  3 + \/ 5  |     ___    |12387    2   4287*\/ 5      |47   46*\/ 5    3*\/ 10 *\/  3 - \/ 5     75*\/ 2 *\/  3 - \/ 5  |   3929*\/ 10 *\/  3 - \/ 5     4645*\/ 2 *\/  3 - \/ 5  |                                            |          /                ___________               /                ___________               ___________    /                ___________              /                ___________               /                ___________               ___________    /                ___________              /                ___________               /                ___________               ___________    /                ___________              /                ___________               /                ___________               ___________    /                ___________              /                ___________               /                ___________               ___________    /                ___________ |       ___    |5217    2   2213*\/ 5      |  48   21*\/ 5    4*\/ 10 *\/  3 + \/ 5     45*\/ 2 *\/  3 + \/ 5  |   3045*\/ 2 *\/  3 + \/ 5     1381*\/ 10 *\/  3 + \/ 5  |                                            |     /                  ___________               /                  ___________                ___________    /                  ___________         /                  ___________               /                  ___________                ___________    /                  ___________         /                  ___________               /                  ___________                ___________    /                  ___________         /                  ___________               /                  ___________                ___________    /                  ___________         /                  ___________               /                  ___________                ___________    /                  ___________ |                                            |     /                  ___________               /                  ___________                ___________    /                  ___________         /                  ___________               /                  ___________                ___________    /                  ___________         /                  ___________               /                  ___________                ___________    /                  ___________         /                  ___________               /                  ___________                ___________    /                  ___________         /                  ___________               /                  ___________                ___________    /                  ___________ |     \/    10     50       |   ___________            ___________      ___________            ___________      ___________            ___________|     \/    10     50       |     ___________            ___________        ___________            ___________        ___________            ___________|                                            |        /                  ___________               /                  ___________                ___________    /                  ___________          /                  ___________               /                  ___________                ___________    /                  ___________          /                  ___________               /                  ___________                ___________    /                  ___________          /                  ___________               /                  ___________                ___________    /                  ___________          /                  ___________               /                  ___________                ___________    /                  ___________ |                                            |        /                  ___________               /                  ___________                ___________    /                  ___________          /                  ___________               /                  ___________                ___________    /                  ___________          /                  ___________               /                  ___________                ___________    /                  ___________          /                  ___________               /                  ___________                ___________    /                  ___________          /                  ___________               /                  ___________                ___________    /                  ___________ |
 |                                                                       |  ____   /         ____   /       ___         ___   /         ____   /       ___         ___   /       ___    /         ____   /       ___       ____   /         ____   /       ___         ___   /         ____   /       ___         ___   /       ___    /         ____   /       ___       ____   /         ____   /       ___         ___   /         ____   /       ___         ___   /       ___    /         ____   /       ___       ____   /         ____   /       ___         ___   /         ____   /       ___         ___   /       ___    /         ____   /       ___       ____   /         ____   /       ___         ___   /         ____   /       ___         ___   /       ___    /         ____   /       ___  |   2*\/ 5 *log|---- + x  - ---------- + x*|- -- + -------- - ----------------------- + -----------------------| - -------------------------- + -------------------------|   |- - -----|*log|-- + x  - ------- + x*|- - + -------- - ----------------------- - ---------------------| - ------------------------ + -----------------------|   |- + -----|*log|-- + x  + ------- + x*|- - - -------- - --------------------- + -----------------------| - ------------------------ - -----------------------|   \/ 5 *log|----- + x  + ---------- + x*|-- + -------- - ----------------------- - -----------------------| - ------------------------- - --------------------------|   \/ 5 *log|----- + x  - ---------- + x*|-- - -------- - ----------------------- + -----------------------| - -------------------------- + -------------------------|                                            |  ____   /         ____   /       ___         ___   /         ____   /       ___         ___   /       ___    /         ____   /       ___       ____   /         ____   /       ___         ___   /         ____   /       ___         ___   /       ___    /         ____   /       ___       ____   /         ____   /       ___         ___   /         ____   /       ___         ___   /       ___    /         ____   /       ___       ____   /         ____   /       ___         ___   /         ____   /       ___         ___   /       ___    /         ____   /       ___       ____   /         ____   /       ___         ___   /         ____   /       ___         ___   /       ___    /         ____   /       ___  |   2*\/ 5 *log|---- + x  + ---------- + x*|- -- - -------- + ----------------------- + -----------------------| - ------------------------- - --------------------------|                                            |    /           ____   /       ___         ___   /           ____   /       ___         ____   /       ___    /           ____   /       ___         /           ____   /       ___         ___   /           ____   /       ___         ____   /       ___    /           ____   /       ___         /           ____   /       ___         ___   /           ____   /       ___         ____   /       ___    /           ____   /       ___         /           ____   /       ___         ___   /           ____   /       ___         ____   /       ___    /           ____   /       ___         /           ____   /       ___         ___   /           ____   /       ___         ____   /       ___    /           ____   /       ___  |                                            |    /           ____   /       ___         ___   /           ____   /       ___         ____   /       ___    /           ____   /       ___         /           ____   /       ___         ___   /           ____   /       ___         ____   /       ___    /           ____   /       ___         /           ____   /       ___         ___   /           ____   /       ___         ____   /       ___    /           ____   /       ___         /           ____   /       ___         ___   /           ____   /       ___         ____   /       ___    /           ____   /       ___         /           ____   /       ___         ___   /           ____   /       ___         ____   /       ___    /           ____   /       ___  |                           |  /       ___      ___   /       ___      /       ___      ___   /       ___      /       ___      ___   /       ___ |                           |    /       ___      ___   /       ___        /       ___      ___   /       ___        /       ___      ___   /       ___ |                                            |       /           ____   /       ___         ___   /           ____   /       ___         ____   /       ___    /           ____   /       ___          /           ____   /       ___         ___   /           ____   /       ___         ____   /       ___    /           ____   /       ___          /           ____   /       ___         ___   /           ____   /       ___         ____   /       ___    /           ____   /       ___          /           ____   /       ___         ___   /           ____   /       ___         ____   /       ___    /           ____   /       ___          /           ____   /       ___         ___   /           ____   /       ___         ____   /       ___    /           ____   /       ___  |                                            |       /           ____   /       ___         ___   /           ____   /       ___         ____   /       ___    /           ____   /       ___          /           ____   /       ___         ___   /           ____   /       ___         ____   /       ___    /           ____   /       ___          /           ____   /       ___         ___   /           ____   /       ___         ____   /       ___    /           ____   /       ___          /           ____   /       ___         ___   /           ____   /       ___         ____   /       ___    /           ____   /       ___          /           ____   /       ___         ___   /           ____   /       ___         ____   /       ___    /           ____   /       ___  |
 |   1             log(1 + x)                                            \\/ 10 *\/   10 - \/ 10 *\/  3 + \/ 5    - 3*\/ 2 *\/   10 - \/ 10 *\/  3 + \/ 5    - 2*\/ 5 *\/  3 + \/ 5  *\/   10 - \/ 10 *\/  3 + \/ 5      \/ 10 *\/   10 - \/ 10 *\/  3 + \/ 5    - 3*\/ 2 *\/   10 - \/ 10 *\/  3 + \/ 5    - 2*\/ 5 *\/  3 + \/ 5  *\/   10 - \/ 10 *\/  3 + \/ 5      \/ 10 *\/   10 - \/ 10 *\/  3 + \/ 5    - 3*\/ 2 *\/   10 - \/ 10 *\/  3 + \/ 5    - 2*\/ 5 *\/  3 + \/ 5  *\/   10 - \/ 10 *\/  3 + \/ 5      \/ 10 *\/   10 - \/ 10 *\/  3 + \/ 5    - 3*\/ 2 *\/   10 - \/ 10 *\/  3 + \/ 5    - 2*\/ 5 *\/  3 + \/ 5  *\/   10 - \/ 10 *\/  3 + \/ 5      \/ 10 *\/   10 - \/ 10 *\/  3 + \/ 5    - 3*\/ 2 *\/   10 - \/ 10 *\/  3 + \/ 5    - 2*\/ 5 *\/  3 + \/ 5  *\/   10 - \/ 10 *\/  3 + \/ 5   /              \242            242         \  11      11                 22                        11          /              484                          484           /   \4     20 /    \16           8        \  8      8                  16                       16         /              64                         64          /   \4     20 /    \16           8        \  8      8                 16                       16          /              64                         64          /            \ 242            242         \11      11                 22                        11          /              484                         484            /            \ 242            242         \11      11                 11                        22          /              484                          484           /                                            \\/ 10 *\/   10 - \/ 10 *\/  3 - \/ 5    + 3*\/ 2 *\/   10 - \/ 10 *\/  3 - \/ 5    + 2*\/ 5 *\/  3 - \/ 5  *\/   10 - \/ 10 *\/  3 - \/ 5      \/ 10 *\/   10 - \/ 10 *\/  3 - \/ 5    + 3*\/ 2 *\/   10 - \/ 10 *\/  3 - \/ 5    + 2*\/ 5 *\/  3 - \/ 5  *\/   10 - \/ 10 *\/  3 - \/ 5      \/ 10 *\/   10 - \/ 10 *\/  3 - \/ 5    + 3*\/ 2 *\/   10 - \/ 10 *\/  3 - \/ 5    + 2*\/ 5 *\/  3 - \/ 5  *\/   10 - \/ 10 *\/  3 - \/ 5      \/ 10 *\/   10 - \/ 10 *\/  3 - \/ 5    + 3*\/ 2 *\/   10 - \/ 10 *\/  3 - \/ 5    + 2*\/ 5 *\/  3 - \/ 5  *\/   10 - \/ 10 *\/  3 - \/ 5      \/ 10 *\/   10 - \/ 10 *\/  3 - \/ 5    + 3*\/ 2 *\/   10 - \/ 10 *\/  3 - \/ 5    + 2*\/ 5 *\/  3 - \/ 5  *\/   10 - \/ 10 *\/  3 - \/ 5   /              \242            242         \  11      11                 11                        22          /              484                         484            /                                            \8*\/   15 - 2*\/ 10 *\/  3 + \/ 5    + 6*\/ 5 *\/   15 - 2*\/ 10 *\/  3 + \/ 5    + 5*\/ 10 *\/  3 + \/ 5  *\/   15 - 2*\/ 10 *\/  3 + \/ 5      8*\/   15 - 2*\/ 10 *\/  3 + \/ 5    + 6*\/ 5 *\/   15 - 2*\/ 10 *\/  3 + \/ 5    + 5*\/ 10 *\/  3 + \/ 5  *\/   15 - 2*\/ 10 *\/  3 + \/ 5      8*\/   15 - 2*\/ 10 *\/  3 + \/ 5    + 6*\/ 5 *\/   15 - 2*\/ 10 *\/  3 + \/ 5    + 5*\/ 10 *\/  3 + \/ 5  *\/   15 - 2*\/ 10 *\/  3 + \/ 5      8*\/   15 - 2*\/ 10 *\/  3 + \/ 5    + 6*\/ 5 *\/   15 - 2*\/ 10 *\/  3 + \/ 5    + 5*\/ 10 *\/  3 + \/ 5  *\/   15 - 2*\/ 10 *\/  3 + \/ 5      8*\/   15 - 2*\/ 10 *\/  3 + \/ 5    + 6*\/ 5 *\/   15 - 2*\/ 10 *\/  3 + \/ 5    + 5*\/ 10 *\/  3 + \/ 5  *\/   15 - 2*\/ 10 *\/  3 + \/ 5   /                                            \8*\/   15 - 2*\/ 10 *\/  3 - \/ 5    - 6*\/ 5 *\/   15 - 2*\/ 10 *\/  3 - \/ 5    + 5*\/ 10 *\/  3 - \/ 5  *\/   15 - 2*\/ 10 *\/  3 - \/ 5      8*\/   15 - 2*\/ 10 *\/  3 - \/ 5    - 6*\/ 5 *\/   15 - 2*\/ 10 *\/  3 - \/ 5    + 5*\/ 10 *\/  3 - \/ 5  *\/   15 - 2*\/ 10 *\/  3 - \/ 5      8*\/   15 - 2*\/ 10 *\/  3 - \/ 5    - 6*\/ 5 *\/   15 - 2*\/ 10 *\/  3 - \/ 5    + 5*\/ 10 *\/  3 - \/ 5  *\/   15 - 2*\/ 10 *\/  3 - \/ 5      8*\/   15 - 2*\/ 10 *\/  3 - \/ 5    - 6*\/ 5 *\/   15 - 2*\/ 10 *\/  3 - \/ 5    + 5*\/ 10 *\/  3 - \/ 5  *\/   15 - 2*\/ 10 *\/  3 - \/ 5      8*\/   15 - 2*\/ 10 *\/  3 - \/ 5    - 6*\/ 5 *\/   15 - 2*\/ 10 *\/  3 - \/ 5    + 5*\/ 10 *\/  3 - \/ 5  *\/   15 - 2*\/ 10 *\/  3 - \/ 5   /                           \\/  5 - \/ 5   + \/ 5 *\/  5 - \/ 5     \/  5 - \/ 5   + \/ 5 *\/  5 - \/ 5     \/  5 - \/ 5   + \/ 5 *\/  5 - \/ 5  /                           \- \/  5 + \/ 5   + \/ 5 *\/  5 + \/ 5     - \/  5 + \/ 5   + \/ 5 *\/  5 + \/ 5     - \/  5 + \/ 5   + \/ 5 *\/  5 + \/ 5  /                                            \  18*\/   15 - 2*\/ 10 *\/  3 + \/ 5    + 8*\/ 5 *\/   15 - 2*\/ 10 *\/  3 + \/ 5    + 3*\/ 10 *\/  3 + \/ 5  *\/   15 - 2*\/ 10 *\/  3 + \/ 5      18*\/   15 - 2*\/ 10 *\/  3 + \/ 5    + 8*\/ 5 *\/   15 - 2*\/ 10 *\/  3 + \/ 5    + 3*\/ 10 *\/  3 + \/ 5  *\/   15 - 2*\/ 10 *\/  3 + \/ 5      18*\/   15 - 2*\/ 10 *\/  3 + \/ 5    + 8*\/ 5 *\/   15 - 2*\/ 10 *\/  3 + \/ 5    + 3*\/ 10 *\/  3 + \/ 5  *\/   15 - 2*\/ 10 *\/  3 + \/ 5      18*\/   15 - 2*\/ 10 *\/  3 + \/ 5    + 8*\/ 5 *\/   15 - 2*\/ 10 *\/  3 + \/ 5    + 3*\/ 10 *\/  3 + \/ 5  *\/   15 - 2*\/ 10 *\/  3 + \/ 5      18*\/   15 - 2*\/ 10 *\/  3 + \/ 5    + 8*\/ 5 *\/   15 - 2*\/ 10 *\/  3 + \/ 5    + 3*\/ 10 *\/  3 + \/ 5  *\/   15 - 2*\/ 10 *\/  3 + \/ 5   /                                            \  18*\/   15 - 2*\/ 10 *\/  3 - \/ 5    - 8*\/ 5 *\/   15 - 2*\/ 10 *\/  3 - \/ 5    + 3*\/ 10 *\/  3 - \/ 5  *\/   15 - 2*\/ 10 *\/  3 - \/ 5      18*\/   15 - 2*\/ 10 *\/  3 - \/ 5    - 8*\/ 5 *\/   15 - 2*\/ 10 *\/  3 - \/ 5    + 3*\/ 10 *\/  3 - \/ 5  *\/   15 - 2*\/ 10 *\/  3 - \/ 5      18*\/   15 - 2*\/ 10 *\/  3 - \/ 5    - 8*\/ 5 *\/   15 - 2*\/ 10 *\/  3 - \/ 5    + 3*\/ 10 *\/  3 - \/ 5  *\/   15 - 2*\/ 10 *\/  3 - \/ 5      18*\/   15 - 2*\/ 10 *\/  3 - \/ 5    - 8*\/ 5 *\/   15 - 2*\/ 10 *\/  3 - \/ 5    + 3*\/ 10 *\/  3 - \/ 5  *\/   15 - 2*\/ 10 *\/  3 - \/ 5      18*\/   15 - 2*\/ 10 *\/  3 - \/ 5    - 8*\/ 5 *\/   15 - 2*\/ 10 *\/  3 - \/ 5    + 3*\/ 10 *\/  3 - \/ 5  *\/   15 - 2*\/ 10 *\/  3 - \/ 5   /
 | ------ dx = C + ---------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
 |  5                  5                                                                                                                                                                                                                                                                                                                                                                                                 5                                                                                                                                                                                                                                                                                                                                                                                                                                                                              25                                                                                                                                                                   5                                                                                                                                                                5                                                                                                                                                                   25                                                                                                                                                                    25                                                                                                                                                                                                                                                                                                                                                                                                                                                                            5                                                                                                                                                                                                                                                                                                                                                                                                                                                                              25                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   5                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               5                                                                                                                                                                                                                                                                                                                                                                                                                                                                        5                                                                                                                                                    5                                                                                                                                                                                                                                                                                                                                                                                                                                                                              5                                                                                                                                                                                                                                                     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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        
 |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           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$$\int \frac{1}{x^{5} + 1}\, dx = C + \frac{\log{\left(x + 1 \right)}}{5} + \frac{2 \sqrt{5} \log{\left(x^{2} + x \left(- \frac{48}{11} - \frac{21 \sqrt{5}}{11} + \frac{4 \sqrt{10} \sqrt{\sqrt{5} + 3}}{11} + \frac{45 \sqrt{2} \sqrt{\sqrt{5} + 3}}{22}\right) - \frac{1381 \sqrt{10} \sqrt{\sqrt{5} + 3}}{484} - \frac{3045 \sqrt{2} \sqrt{\sqrt{5} + 3}}{484} + \frac{2213 \sqrt{5}}{242} + \frac{5217}{242} \right)}}{25} - \frac{2 \sqrt{5} \log{\left(x^{2} + x \left(- \frac{48}{11} - \frac{45 \sqrt{2} \sqrt{3 - \sqrt{5}}}{22} + \frac{4 \sqrt{10} \sqrt{3 - \sqrt{5}}}{11} + \frac{21 \sqrt{5}}{11}\right) - \frac{2213 \sqrt{5}}{242} - \frac{1381 \sqrt{10} \sqrt{3 - \sqrt{5}}}{484} + \frac{3045 \sqrt{2} \sqrt{3 - \sqrt{5}}}{484} + \frac{5217}{242} \right)}}{25} + \frac{\sqrt{5} \log{\left(x^{2} + x \left(- \frac{46 \sqrt{5}}{11} - \frac{3 \sqrt{10} \sqrt{3 - \sqrt{5}}}{11} + \frac{75 \sqrt{2} \sqrt{3 - \sqrt{5}}}{22} + \frac{47}{11}\right) - \frac{4287 \sqrt{5}}{242} - \frac{3929 \sqrt{10} \sqrt{3 - \sqrt{5}}}{484} + \frac{4645 \sqrt{2} \sqrt{3 - \sqrt{5}}}{484} + \frac{12387}{242} \right)}}{25} - \frac{\left(\frac{\sqrt{5}}{20} + \frac{1}{4}\right) \log{\left(x^{2} + x \left(- \frac{11 \sqrt{5}}{8} - \frac{9}{8} - \frac{\sqrt{10} \sqrt{\sqrt{5} + 3}}{16} + \frac{15 \sqrt{2} \sqrt{\sqrt{5} + 3}}{16}\right) - \frac{37 \sqrt{10} \sqrt{\sqrt{5} + 3}}{64} - \frac{35 \sqrt{2} \sqrt{\sqrt{5} + 3}}{64} + \frac{9 \sqrt{5}}{8} + \frac{71}{16} \right)}}{5} - \frac{\left(\frac{1}{4} - \frac{\sqrt{5}}{20}\right) \log{\left(x^{2} + x \left(- \frac{15 \sqrt{2} \sqrt{3 - \sqrt{5}}}{16} - \frac{9}{8} - \frac{\sqrt{10} \sqrt{3 - \sqrt{5}}}{16} + \frac{11 \sqrt{5}}{8}\right) - \frac{9 \sqrt{5}}{8} - \frac{37 \sqrt{10} \sqrt{3 - \sqrt{5}}}{64} + \frac{35 \sqrt{2} \sqrt{3 - \sqrt{5}}}{64} + \frac{71}{16} \right)}}{5} - \frac{\sqrt{5} \log{\left(x^{2} + x \left(- \frac{75 \sqrt{2} \sqrt{\sqrt{5} + 3}}{22} - \frac{3 \sqrt{10} \sqrt{\sqrt{5} + 3}}{11} + \frac{47}{11} + \frac{46 \sqrt{5}}{11}\right) - \frac{3929 \sqrt{10} \sqrt{\sqrt{5} + 3}}{484} - \frac{4645 \sqrt{2} \sqrt{\sqrt{5} + 3}}{484} + \frac{4287 \sqrt{5}}{242} + \frac{12387}{242} \right)}}{25} + \frac{6 \sqrt{\frac{1}{10} - \frac{\sqrt{5}}{50}} \operatorname{atan}{\left(\frac{4 \sqrt{2} x}{\sqrt{5 - \sqrt{5}} + \sqrt{5} \sqrt{5 - \sqrt{5}}} - \frac{\sqrt{2}}{\sqrt{5 - \sqrt{5}} + \sqrt{5} \sqrt{5 - \sqrt{5}}} + \frac{\sqrt{10}}{\sqrt{5 - \sqrt{5}} + \sqrt{5} \sqrt{5 - \sqrt{5}}} \right)}}{5} + \frac{6 \sqrt{\frac{\sqrt{5}}{50} + \frac{1}{10}} \operatorname{atan}{\left(- \frac{4 \sqrt{2} x}{- \sqrt{\sqrt{5} + 5} + \sqrt{5} \sqrt{\sqrt{5} + 5}} + \frac{\sqrt{2}}{- \sqrt{\sqrt{5} + 5} + \sqrt{5} \sqrt{\sqrt{5} + 5}} + \frac{\sqrt{10}}{- \sqrt{\sqrt{5} + 5} + \sqrt{5} \sqrt{\sqrt{5} + 5}} \right)}}{5} + \frac{2 \sqrt{- \frac{\sqrt{10} \sqrt{3 - \sqrt{5}}}{200} + \frac{1}{20}} \operatorname{atan}{\left(- \frac{32 x}{\sqrt{10} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 2 \sqrt{5} \sqrt{3 - \sqrt{5}} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10}} - \frac{22 \sqrt{5}}{\sqrt{10} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 2 \sqrt{5} \sqrt{3 - \sqrt{5}} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10}} + \frac{\sqrt{10} \sqrt{3 - \sqrt{5}}}{\sqrt{10} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 2 \sqrt{5} \sqrt{3 - \sqrt{5}} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10}} + \frac{18}{\sqrt{10} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 2 \sqrt{5} \sqrt{3 - \sqrt{5}} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10}} + \frac{15 \sqrt{2} \sqrt{3 - \sqrt{5}}}{\sqrt{10} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 2 \sqrt{5} \sqrt{3 - \sqrt{5}} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10}} \right)}}{5} + \frac{8 \sqrt{- \frac{\sqrt{10} \sqrt{3 - \sqrt{5}}}{50} + \frac{3}{20}} \operatorname{atan}{\left(\frac{44 x}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} - \frac{96}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} - \frac{45 \sqrt{2} \sqrt{3 - \sqrt{5}}}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} + \frac{8 \sqrt{10} \sqrt{3 - \sqrt{5}}}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} + \frac{42 \sqrt{5}}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} \right)}}{5} + \frac{4 \sqrt{- \frac{\sqrt{10} \sqrt{3 - \sqrt{5}}}{50} + \frac{3}{20}} \operatorname{atan}{\left(\frac{44 x}{- 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 8 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 5 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} - \frac{92 \sqrt{5}}{- 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 8 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 5 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} - \frac{6 \sqrt{10} \sqrt{3 - \sqrt{5}}}{- 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 8 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 5 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} + \frac{75 \sqrt{2} \sqrt{3 - \sqrt{5}}}{- 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 8 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 5 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} + \frac{94}{- 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 8 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 5 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} \right)}}{5} + \frac{8 \sqrt{- \frac{\sqrt{10} \sqrt{\sqrt{5} + 3}}{50} + \frac{3}{20}} \operatorname{atan}{\left(\frac{44 x}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} - \frac{96}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} - \frac{42 \sqrt{5}}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} + \frac{8 \sqrt{10} \sqrt{\sqrt{5} + 3}}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} + \frac{45 \sqrt{2} \sqrt{\sqrt{5} + 3}}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} \right)}}{5} - \frac{2 \sqrt{- \frac{\sqrt{10} \sqrt{\sqrt{5} + 3}}{200} + \frac{1}{20}} \operatorname{atan}{\left(- \frac{32 x}{- 2 \sqrt{5} \sqrt{\sqrt{5} + 3} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} - 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} + \sqrt{10} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10}} + \frac{22 \sqrt{5}}{- 2 \sqrt{5} \sqrt{\sqrt{5} + 3} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} - 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} + \sqrt{10} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10}} + \frac{18}{- 2 \sqrt{5} \sqrt{\sqrt{5} + 3} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} - 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} + \sqrt{10} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10}} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 3}}{- 2 \sqrt{5} \sqrt{\sqrt{5} + 3} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} - 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} + \sqrt{10} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10}} - \frac{15 \sqrt{2} \sqrt{\sqrt{5} + 3}}{- 2 \sqrt{5} \sqrt{\sqrt{5} + 3} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} - 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} + \sqrt{10} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10}} \right)}}{5} + \frac{4 \sqrt{- \frac{\sqrt{10} \sqrt{\sqrt{5} + 3}}{50} + \frac{3}{20}} \operatorname{atan}{\left(\frac{44 x}{8 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 5 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} - \frac{75 \sqrt{2} \sqrt{\sqrt{5} + 3}}{8 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 5 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} - \frac{6 \sqrt{10} \sqrt{\sqrt{5} + 3}}{8 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 5 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} + \frac{94}{8 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 5 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} + \frac{92 \sqrt{5}}{8 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 5 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} \right)}}{5}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
         /     4        3       2                           \   log(2)          /     4        3       2                               \
- RootSum\625*t  + 125*t  + 25*t  + 5*t + 1, t -> t*log(5*t)/ + ------ + RootSum\625*t  + 125*t  + 25*t  + 5*t + 1, t -> t*log(1 + 5*t)/
                                                                  5
$$- \operatorname{RootSum} {\left(625 t^{4} + 125 t^{3} + 25 t^{2} + 5 t + 1, \left( t \mapsto t \log{\left(5 t \right)} \right)\right)} + \operatorname{RootSum} {\left(625 t^{4} + 125 t^{3} + 25 t^{2} + 5 t + 1, \left( t \mapsto t \log{\left(5 t + 1 \right)} \right)\right)} + \frac{\log{\left(2 \right)}}{5}$$ 
=
= 
         /     4        3       2                           \   log(2)          /     4        3       2                               \
- RootSum\625*t  + 125*t  + 25*t  + 5*t + 1, t -> t*log(5*t)/ + ------ + RootSum\625*t  + 125*t  + 25*t  + 5*t + 1, t -> t*log(1 + 5*t)/
                                                                  5
$$- \operatorname{RootSum} {\left(625 t^{4} + 125 t^{3} + 25 t^{2} + 5 t + 1, \left( t \mapsto t \log{\left(5 t \right)} \right)\right)} + \operatorname{RootSum} {\left(625 t^{4} + 125 t^{3} + 25 t^{2} + 5 t + 1, \left( t \mapsto t \log{\left(5 t + 1 \right)} \right)\right)} + \frac{\log{\left(2 \right)}}{5}$$ 
-RootSum(625*_t^4 + 125*_t^3 + 25*_t^2 + 5*_t + 1, Lambda(_t, _t*log(5*_t))) + log(2)/5 + RootSum(625*_t^4 + 125*_t^3 + 25*_t^2 + 5*_t + 1, Lambda(_t, _t*log(1 + 5*_t)))
Respuesta numérica [src] 
0.888313572651789
0.888313572651789

    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

    © Sr Examen