Общий множитель x^3-x-3*x^5/5+x^7/7

Комбинаторика

  /          4      6       2\
x*\-35 - 21*x  + 5*x  + 35*x /
------------------------------
              35              

$$\frac{x \left(5 x^{6} - 21 x^{4} + 35 x^{2} - 35\right)}{35}$$

Объединение рациональных выражений

  /          4      6       2\
x*\-35 - 21*x  + 5*x  + 35*x /
------------------------------
              35              

$$\frac{x \left(5 x^{6} - 21 x^{4} + 35 x^{2} - 35\right)}{35}$$

Разложение на множители

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                                                                                                                                                                        |                                                                                                                                                     |    |                       6 ___  2/3                                         5/6 3 ___ 3 /          ____                ||                                                                                                                                                      |    |                       6 ___  2/3                                         5/6 3 ___ 3 /          ____                ||| |                                                                                                                                                     |    |                       6 ___  2/3                                         5/6 3 ___ 3 /          ____                ||                                                                                                                                                      |    |                       6 ___  2/3                                         5/6 3 ___ 3 /          ____                ||| |                                                                                                                                                       |    |                       6 ___  2/3                                         5/6 3 ___ 3 /          ____                ||                                                                                                                                                      |    |                       6 ___  2/3                                         5/6 3 ___ 3 /          ____                ||| |                                                                                                                                                       |    |                       6 ___  2/3                                         5/6 3 ___ 3 /          ____                ||                                                                                                                                                      |    |                       6 ___  2/3                                         5/6 3 ___ 3 /          ____                |||
                                                                                                                                                                        |                                                                                                                                                     |    |                       \/ 3 *7                                           3   *\/ 7 *\/  27 + 5*\/ 30                 ||                                                                                                                                                      |    |                       \/ 3 *7                                           3   *\/ 7 *\/  27 + 5*\/ 30                 ||| |                                                                                                                                                     |    |                       \/ 3 *7                                           3   *\/ 7 *\/  27 + 5*\/ 30                 ||                                                                                                                                                      |    |                       \/ 3 *7                                           3   *\/ 7 *\/  27 + 5*\/ 30                 ||| |                                                                                                                                                       |    |                       \/ 3 *7                                           3   *\/ 7 *\/  27 + 5*\/ 30                 ||                                                                                                                                                      |    |                       \/ 3 *7                                           3   *\/ 7 *\/  27 + 5*\/ 30                 ||| |                                                                                                                                                       |    |                       \/ 3 *7                                           3   *\/ 7 *\/  27 + 5*\/ 30                 ||                                                                                                                                                      |    |                       \/ 3 *7                                           3   *\/ 7 *\/  27 + 5*\/ 30                 |||
                                                                                                                                                                        |                                                                                                                                                     |atan|-------------------------------------------------------- + ----------------------------------------------------------||                                                                                                                                                      |atan|-------------------------------------------------------- + ----------------------------------------------------------||| |                                                                                                                                                     |atan|-------------------------------------------------------- + ----------------------------------------------------------||                                                                                                                                                      |atan|-------------------------------------------------------- + ----------------------------------------------------------||| |                                                                                                                                                       |atan|-------------------------------------------------------- + ----------------------------------------------------------||                                                                                                                                                      |atan|-------------------------------------------------------- + ----------------------------------------------------------||| |                                                                                                                                                       |atan|-------------------------------------------------------- + ----------------------------------------------------------||                                                                                                                                                      |atan|-------------------------------------------------------- + ----------------------------------------------------------|||
                                                                                                                                                                        |                                                                                                                                                     |    |                                                     2/3      /              _______________                        \||                                                                                                                                                      |    |                                                     2/3      /              _______________                        \||| |                                                                                                                                                     |    |                                                     2/3      /              _______________                        \||                                                                                                                                                      |    |                                                     2/3      /              _______________                        \||| |                                                                                                                                                       |    |                                                     2/3      /              _______________                        \||                                                                                                                                                      |    |                                                     2/3      /              _______________                        \||| |                                                                                                                                                       |    |                                                     2/3      /              _______________                        \||                                                                                                                                                      |    |                                                     2/3      /              _______________                        \|||
                                                                                                                                                                        |                                                                                                                                                     |    |     _______________     2/3   3 ____ /         ____\         |    3 ____ 3 /          ____              2/3        |||                                                                                                                                                      |    |     _______________     2/3   3 ____ /         ____\         |    3 ____ 3 /          ____              2/3        |||| |                                                                                                                                                     |    |     _______________     2/3   3 ____ /         ____\         |    3 ____ 3 /          ____              2/3        |||                                                                                                                                                      |    |     _______________     2/3   3 ____ /         ____\         |    3 ____ 3 /          ____              2/3        |||| |                                                                                                                                                       |    |     _______________     2/3   3 ____ /         ____\         |    3 ____ 3 /          ____              2/3        |||                                                                                                                                                      |    |     _______________     2/3   3 ____ /         ____\         |    3 ____ 3 /          ____              2/3        |||| |                                                                                                                                                       |    |     _______________     2/3   3 ____ /         ____\         |    3 ____ 3 /          ____              2/3        |||                                                                                                                                                      |    |     _______________     2/3   3 ____ /         ____\         |    3 ____ 3 /          ____              2/3        ||||
                                                                                                                                                                        |                                                                                                                                                     |    |  3 /          ____    21      \/ 21 *\27 + 5*\/ 30 /         |7   \/ 21 *\/  27 + 5*\/ 30             21           |||                                                                                                                                                      |    |  3 /          ____    21      \/ 21 *\27 + 5*\/ 30 /         |7   \/ 21 *\/  27 + 5*\/ 30             21           |||| |                                                                                                                                                     |    |  3 /          ____    21      \/ 21 *\27 + 5*\/ 30 /         |7   \/ 21 *\/  27 + 5*\/ 30             21           |||                                                                                                                                                      |    |  3 /          ____    21      \/ 21 *\27 + 5*\/ 30 /         |7   \/ 21 *\/  27 + 5*\/ 30             21           |||| |                                                                                                                                                       |    |  3 /          ____    21      \/ 21 *\27 + 5*\/ 30 /         |7   \/ 21 *\/  27 + 5*\/ 30             21           |||                                                                                                                                                      |    |  3 /          ____    21      \/ 21 *\27 + 5*\/ 30 /         |7   \/ 21 *\/  27 + 5*\/ 30             21           |||| |                                                                                                                                                       |    |  3 /          ____    21      \/ 21 *\27 + 5*\/ 30 /         |7   \/ 21 *\/  27 + 5*\/ 30             21           |||                                                                                                                                                      |    |  3 /          ____    21      \/ 21 *\27 + 5*\/ 30 /         |7   \/ 21 *\/  27 + 5*\/ 30             21           ||||
  /               _________________________________________________________________\ /               _________________________________________________________________\ |            _____________________________________________________________________________________________________________________________________    |    |7*\/  27 + 5*\/ 30   + ----- - -------------------------   15*|- - ------------------------- + ---------------------|||             _____________________________________________________________________________________________________________________________________    |    |7*\/  27 + 5*\/ 30   + ----- - -------------------------   15*|- - ------------------------- + ---------------------|||| |            _____________________________________________________________________________________________________________________________________    |    |7*\/  27 + 5*\/ 30   + ----- - -------------------------   15*|- - ------------------------- + ---------------------|||             _____________________________________________________________________________________________________________________________________    |    |7*\/  27 + 5*\/ 30   + ----- - -------------------------   15*|- - ------------------------- + ---------------------|||| |              _____________________________________________________________________________________________________________________________________    |    |7*\/  27 + 5*\/ 30   + ----- - -------------------------   15*|- - ------------------------- + ---------------------|||             _____________________________________________________________________________________________________________________________________    |    |7*\/  27 + 5*\/ 30   + ----- - -------------------------   15*|- - ------------------------- + ---------------------|||| |              _____________________________________________________________________________________________________________________________________    |    |7*\/  27 + 5*\/ 30   + ----- - -------------------------   15*|- - ------------------------- + ---------------------|||             _____________________________________________________________________________________________________________________________________    |    |7*\/  27 + 5*\/ 30   + ----- - -------------------------   15*|- - ------------------------- + ---------------------||||
  |              /                   _______________                           2/3 | |              /                   _______________                           2/3 | |           /                                                    2/3               _______________                                                    |    |                         3                 3                  |5               15                    _______________|||            /                                                    2/3               _______________                                                    |    |                         3                 3                  |5               15                    _______________|||| |           /                                                    2/3               _______________                                                    |    |                         3                 3                  |5               15                    _______________|||            /                                                    2/3               _______________                                                    |    |                         3                 3                  |5               15                    _______________|||| |             /                                                    2/3               _______________                                                    |    |                         3                 3                  |5               15                    _______________|||            /                                                    2/3               _______________                                                    |    |                         3                 3                  |5               15                    _______________|||| |             /                                                    2/3               _______________                                                    |    |                         3                 3                  |5               15                    _______________|||            /                                                    2/3               _______________                                                    |    |                         3                 3                  |5               15                    _______________||||
  |      ____   /        2/3      3 /          ____      3 ____ /         ____\    | |      ____   /        2/3      3 /          ____      3 ____ /         ____\    | |          /                3 ____            2/3 /         ____\        3 ____ 3 /          ____                2/3            5/6 3 ___   ____      |    |                                                              |                                   3 /          ____ |||           /                3 ____            2/3 /         ____\        3 ____ 3 /          ____                2/3            5/6 3 ___   ____      |    |                                                              |                                   3 /          ____ |||| |          /                3 ____            2/3 /         ____\        3 ____ 3 /          ____                2/3            5/6 3 ___   ____      |    |                                                              |                                   3 /          ____ |||           /                3 ____            2/3 /         ____\        3 ____ 3 /          ____                2/3            5/6 3 ___   ____      |    |                                                              |                                   3 /          ____ |||| |            /                3 ____            2/3 /         ____\        3 ____ 3 /          ____                2/3            5/6 3 ___   ____      |    |                                                              |                                   3 /          ____ |||           /                3 ____            2/3 /         ____\        3 ____ 3 /          ____                2/3            5/6 3 ___   ____      |    |                                                              |                                   3 /          ____ |||| |            /                3 ____            2/3 /         ____\        3 ____ 3 /          ____                2/3            5/6 3 ___   ____      |    |                                                              |                                   3 /          ____ |||           /                3 ____            2/3 /         ____\        3 ____ 3 /          ____                2/3            5/6 3 ___   ____      |    |                                                              |                                   3 /          ____ ||||
  |    \/ 15 *\/   - 2*21    + 21*\/  27 + 5*\/ 30   + 2*\/ 21 *\27 + 5*\/ 30 /    | |    \/ 15 *\/   - 2*21    + 21*\/  27 + 5*\/ 30   + 2*\/ 21 *\27 + 5*\/ 30 /    | |         /   7         539*\/ 21         4*21   *\27 + 5*\/ 30 /      7*\/ 21 *\/  27 + 5*\/ 30            14*21            7*3   *\/ 7 *\/ 10       |    \                                                              \                                15*\/  27 + 5*\/ 30  //|          /   7         539*\/ 21         4*21   *\27 + 5*\/ 30 /      7*\/ 21 *\/  27 + 5*\/ 30            14*21            7*3   *\/ 7 *\/ 10       |    \                                                              \                                15*\/  27 + 5*\/ 30  //|| |         /   7         539*\/ 21         4*21   *\27 + 5*\/ 30 /      7*\/ 21 *\/  27 + 5*\/ 30            14*21            7*3   *\/ 7 *\/ 10       |    \                                                              \                                15*\/  27 + 5*\/ 30  //|          /   7         539*\/ 21         4*21   *\27 + 5*\/ 30 /      7*\/ 21 *\/  27 + 5*\/ 30            14*21            7*3   *\/ 7 *\/ 10       |    \                                                              \                                15*\/  27 + 5*\/ 30  //|| |           /   7         539*\/ 21         4*21   *\27 + 5*\/ 30 /      7*\/ 21 *\/  27 + 5*\/ 30            14*21            7*3   *\/ 7 *\/ 10       |    \                                                              \                                15*\/  27 + 5*\/ 30  //|          /   7         539*\/ 21         4*21   *\27 + 5*\/ 30 /      7*\/ 21 *\/  27 + 5*\/ 30            14*21            7*3   *\/ 7 *\/ 10       |    \                                                              \                                15*\/  27 + 5*\/ 30  //|| |           /   7         539*\/ 21         4*21   *\27 + 5*\/ 30 /      7*\/ 21 *\/  27 + 5*\/ 30            14*21            7*3   *\/ 7 *\/ 10       |    \                                                              \                                15*\/  27 + 5*\/ 30  //|          /   7         539*\/ 21         4*21   *\27 + 5*\/ 30 /      7*\/ 21 *\/  27 + 5*\/ 30            14*21            7*3   *\/ 7 *\/ 10       |    \                                                              \                                15*\/  27 + 5*\/ 30  //||
x*|x + ----------------------------------------------------------------------------|*|x - ----------------------------------------------------------------------------|*|x +     /    - - --------------------- + -------------------------- + --------------------------- + --------------------- - -------------------- *cos|---------------------------------------------------------------------------------------------------------------------------| + I*    /    - - --------------------- + -------------------------- + --------------------------- + --------------------- - -------------------- *sin|---------------------------------------------------------------------------------------------------------------------------||*|x +     /    - - --------------------- + -------------------------- + --------------------------- + --------------------- - -------------------- *cos|---------------------------------------------------------------------------------------------------------------------------| - I*    /    - - --------------------- + -------------------------- + --------------------------- + --------------------- - -------------------- *sin|---------------------------------------------------------------------------------------------------------------------------||*|x + -     /    - - --------------------- + -------------------------- + --------------------------- + --------------------- - -------------------- *cos|---------------------------------------------------------------------------------------------------------------------------| + I*    /    - - --------------------- + -------------------------- + --------------------------- + --------------------- - -------------------- *sin|---------------------------------------------------------------------------------------------------------------------------||*|x + -     /    - - --------------------- + -------------------------- + --------------------------- + --------------------- - -------------------- *cos|---------------------------------------------------------------------------------------------------------------------------| - I*    /    - - --------------------- + -------------------------- + --------------------------- + --------------------- - -------------------- *sin|---------------------------------------------------------------------------------------------------------------------------||
  |                                     _______________                            | |                                     _______________                            | |       /     3                     2/3              225                            75                     _______________                    2/3     \                                                             2                                                             /        /     3                     2/3              225                            75                     _______________                    2/3     \                                                             2                                                             /| |       /     3                     2/3              225                            75                     _______________                    2/3     \                                                             2                                                             /        /     3                     2/3              225                            75                     _______________                    2/3     \                                                             2                                                             /| |         /     3                     2/3              225                            75                     _______________                    2/3     \                                                             2                                                             /        /     3                     2/3              225                            75                     _______________                    2/3     \                                                             2                                                             /| |         /     3                     2/3              225                            75                     _______________                    2/3     \                                                             2                                                             /        /     3                     2/3              225                            75                     _______________                    2/3     \                                                             2                                                             /|
  |                                  6 /          ____                             | |                                  6 /          ____                             | |    4 /             /         ____\                                                                    3 /          ____      /         ____\                                                                                                                                          4 /             /         ____\                                                                    3 /          ____      /         ____\                                                                                                                                     | |    4 /             /         ____\                                                                    3 /          ____      /         ____\                                                                                                                                          4 /             /         ____\                                                                    3 /          ____      /         ____\                                                                                                                                     | |      4 /             /         ____\                                                                    3 /          ____      /         ____\                                                                                                                                          4 /             /         ____\                                                                    3 /          ____      /         ____\                                                                                                                                     | |      4 /             /         ____\                                                                    3 /          ____      /         ____\                                                                                                                                          4 /             /         ____\                                                                    3 /          ____      /         ____\                                                                                                                                     |
  \                               15*\/  27 + 5*\/ 30                              / \                               15*\/  27 + 5*\/ 30                              / \    \/           75*\27 + 5*\/ 30 /                                                                 75*\/  27 + 5*\/ 30     5*\27 + 5*\/ 30 /                                                                                                                                          \/           75*\27 + 5*\/ 30 /                                                                 75*\/  27 + 5*\/ 30     5*\27 + 5*\/ 30 /                                                                                                                                     / \    \/           75*\27 + 5*\/ 30 /                                                                 75*\/  27 + 5*\/ 30     5*\27 + 5*\/ 30 /                                                                                                                                          \/           75*\27 + 5*\/ 30 /                                                                 75*\/  27 + 5*\/ 30     5*\27 + 5*\/ 30 /                                                                                                                                     / \      \/           75*\27 + 5*\/ 30 /                                                                 75*\/  27 + 5*\/ 30     5*\27 + 5*\/ 30 /                                                                                                                                          \/           75*\27 + 5*\/ 30 /                                                                 75*\/  27 + 5*\/ 30     5*\27 + 5*\/ 30 /                                                                                                                                     / \      \/           75*\27 + 5*\/ 30 /                                                                 75*\/  27 + 5*\/ 30     5*\27 + 5*\/ 30 /                                                                                                                                          \/           75*\27 + 5*\/ 30 /                                                                 75*\/  27 + 5*\/ 30     5*\27 + 5*\/ 30 /                                                                                                                                     /

$$x \left(x + \frac{\sqrt{15} \sqrt{- 2 \cdot 21^{\frac{2}{3}} + 2 \sqrt[3]{21} \left(27 + 5 \sqrt{30}\right)^{\frac{2}{3}} + 21 \sqrt[3]{27 + 5 \sqrt{30}}}}{15 \sqrt[6]{27 + 5 \sqrt{30}}}\right) \left(x - \frac{\sqrt{15} \sqrt{- 2 \cdot 21^{\frac{2}{3}} + 2 \sqrt[3]{21} \left(27 + 5 \sqrt{30}\right)^{\frac{2}{3}} + 21 \sqrt[3]{27 + 5 \sqrt{30}}}}{15 \sqrt[6]{27 + 5 \sqrt{30}}}\right) \left(x + \left(\sqrt[4]{- \frac{7 \sqrt{10} \cdot 3^{\frac{5}{6}} \sqrt[3]{7}}{5 \left(27 + 5 \sqrt{30}\right)^{\frac{2}{3}}} - \frac{539 \sqrt[3]{21}}{75 \left(27 + 5 \sqrt{30}\right)^{\frac{2}{3}}} + \frac{14 \cdot 21^{\frac{2}{3}}}{75 \sqrt[3]{27 + 5 \sqrt{30}}} + \frac{7 \sqrt[3]{21} \sqrt[3]{27 + 5 \sqrt{30}}}{75} + \frac{4 \cdot 21^{\frac{2}{3}} \left(27 + 5 \sqrt{30}\right)^{\frac{2}{3}}}{225} + \frac{7}{3}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt[6]{3} \cdot 7^{\frac{2}{3}}}{- \frac{\sqrt[3]{21} \left(27 + 5 \sqrt{30}\right)^{\frac{2}{3}}}{3} + \frac{21^{\frac{2}{3}}}{3} + 7 \sqrt[3]{27 + 5 \sqrt{30}}} + \frac{3^{\frac{5}{6}} \sqrt[3]{7} \sqrt[3]{27 + 5 \sqrt{30}}}{15 \left(- \frac{\sqrt[3]{21} \sqrt[3]{27 + 5 \sqrt{30}}}{15} + \frac{21^{\frac{2}{3}}}{15 \sqrt[3]{27 + 5 \sqrt{30}}} + \frac{7}{5}\right)} \right)}}{2} \right)} + i \sqrt[4]{- \frac{7 \sqrt{10} \cdot 3^{\frac{5}{6}} \sqrt[3]{7}}{5 \left(27 + 5 \sqrt{30}\right)^{\frac{2}{3}}} - \frac{539 \sqrt[3]{21}}{75 \left(27 + 5 \sqrt{30}\right)^{\frac{2}{3}}} + \frac{14 \cdot 21^{\frac{2}{3}}}{75 \sqrt[3]{27 + 5 \sqrt{30}}} + \frac{7 \sqrt[3]{21} \sqrt[3]{27 + 5 \sqrt{30}}}{75} + \frac{4 \cdot 21^{\frac{2}{3}} \left(27 + 5 \sqrt{30}\right)^{\frac{2}{3}}}{225} + \frac{7}{3}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt[6]{3} \cdot 7^{\frac{2}{3}}}{- \frac{\sqrt[3]{21} \left(27 + 5 \sqrt{30}\right)^{\frac{2}{3}}}{3} + \frac{21^{\frac{2}{3}}}{3} + 7 \sqrt[3]{27 + 5 \sqrt{30}}} + \frac{3^{\frac{5}{6}} \sqrt[3]{7} \sqrt[3]{27 + 5 \sqrt{30}}}{15 \left(- \frac{\sqrt[3]{21} \sqrt[3]{27 + 5 \sqrt{30}}}{15} + \frac{21^{\frac{2}{3}}}{15 \sqrt[3]{27 + 5 \sqrt{30}}} + \frac{7}{5}\right)} \right)}}{2} \right)}\right)\right) \left(x + \left(\sqrt[4]{- \frac{7 \sqrt{10} \cdot 3^{\frac{5}{6}} \sqrt[3]{7}}{5 \left(27 + 5 \sqrt{30}\right)^{\frac{2}{3}}} - \frac{539 \sqrt[3]{21}}{75 \left(27 + 5 \sqrt{30}\right)^{\frac{2}{3}}} + \frac{14 \cdot 21^{\frac{2}{3}}}{75 \sqrt[3]{27 + 5 \sqrt{30}}} + \frac{7 \sqrt[3]{21} \sqrt[3]{27 + 5 \sqrt{30}}}{75} + \frac{4 \cdot 21^{\frac{2}{3}} \left(27 + 5 \sqrt{30}\right)^{\frac{2}{3}}}{225} + \frac{7}{3}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt[6]{3} \cdot 7^{\frac{2}{3}}}{- \frac{\sqrt[3]{21} \left(27 + 5 \sqrt{30}\right)^{\frac{2}{3}}}{3} + \frac{21^{\frac{2}{3}}}{3} + 7 \sqrt[3]{27 + 5 \sqrt{30}}} + \frac{3^{\frac{5}{6}} \sqrt[3]{7} \sqrt[3]{27 + 5 \sqrt{30}}}{15 \left(- \frac{\sqrt[3]{21} \sqrt[3]{27 + 5 \sqrt{30}}}{15} + \frac{21^{\frac{2}{3}}}{15 \sqrt[3]{27 + 5 \sqrt{30}}} + \frac{7}{5}\right)} \right)}}{2} \right)} - i \sqrt[4]{- \frac{7 \sqrt{10} \cdot 3^{\frac{5}{6}} \sqrt[3]{7}}{5 \left(27 + 5 \sqrt{30}\right)^{\frac{2}{3}}} - \frac{539 \sqrt[3]{21}}{75 \left(27 + 5 \sqrt{30}\right)^{\frac{2}{3}}} + \frac{14 \cdot 21^{\frac{2}{3}}}{75 \sqrt[3]{27 + 5 \sqrt{30}}} + \frac{7 \sqrt[3]{21} \sqrt[3]{27 + 5 \sqrt{30}}}{75} + \frac{4 \cdot 21^{\frac{2}{3}} \left(27 + 5 \sqrt{30}\right)^{\frac{2}{3}}}{225} + \frac{7}{3}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt[6]{3} \cdot 7^{\frac{2}{3}}}{- \frac{\sqrt[3]{21} \left(27 + 5 \sqrt{30}\right)^{\frac{2}{3}}}{3} + \frac{21^{\frac{2}{3}}}{3} + 7 \sqrt[3]{27 + 5 \sqrt{30}}} + \frac{3^{\frac{5}{6}} \sqrt[3]{7} \sqrt[3]{27 + 5 \sqrt{30}}}{15 \left(- \frac{\sqrt[3]{21} \sqrt[3]{27 + 5 \sqrt{30}}}{15} + \frac{21^{\frac{2}{3}}}{15 \sqrt[3]{27 + 5 \sqrt{30}}} + \frac{7}{5}\right)} \right)}}{2} \right)}\right)\right) \left(x + \left(- \sqrt[4]{- \frac{7 \sqrt{10} \cdot 3^{\frac{5}{6}} \sqrt[3]{7}}{5 \left(27 + 5 \sqrt{30}\right)^{\frac{2}{3}}} - \frac{539 \sqrt[3]{21}}{75 \left(27 + 5 \sqrt{30}\right)^{\frac{2}{3}}} + \frac{14 \cdot 21^{\frac{2}{3}}}{75 \sqrt[3]{27 + 5 \sqrt{30}}} + \frac{7 \sqrt[3]{21} \sqrt[3]{27 + 5 \sqrt{30}}}{75} + \frac{4 \cdot 21^{\frac{2}{3}} \left(27 + 5 \sqrt{30}\right)^{\frac{2}{3}}}{225} + \frac{7}{3}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt[6]{3} \cdot 7^{\frac{2}{3}}}{- \frac{\sqrt[3]{21} \left(27 + 5 \sqrt{30}\right)^{\frac{2}{3}}}{3} + \frac{21^{\frac{2}{3}}}{3} + 7 \sqrt[3]{27 + 5 \sqrt{30}}} + \frac{3^{\frac{5}{6}} \sqrt[3]{7} \sqrt[3]{27 + 5 \sqrt{30}}}{15 \left(- \frac{\sqrt[3]{21} \sqrt[3]{27 + 5 \sqrt{30}}}{15} + \frac{21^{\frac{2}{3}}}{15 \sqrt[3]{27 + 5 \sqrt{30}}} + \frac{7}{5}\right)} \right)}}{2} \right)} + i \sqrt[4]{- \frac{7 \sqrt{10} \cdot 3^{\frac{5}{6}} \sqrt[3]{7}}{5 \left(27 + 5 \sqrt{30}\right)^{\frac{2}{3}}} - \frac{539 \sqrt[3]{21}}{75 \left(27 + 5 \sqrt{30}\right)^{\frac{2}{3}}} + \frac{14 \cdot 21^{\frac{2}{3}}}{75 \sqrt[3]{27 + 5 \sqrt{30}}} + \frac{7 \sqrt[3]{21} \sqrt[3]{27 + 5 \sqrt{30}}}{75} + \frac{4 \cdot 21^{\frac{2}{3}} \left(27 + 5 \sqrt{30}\right)^{\frac{2}{3}}}{225} + \frac{7}{3}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt[6]{3} \cdot 7^{\frac{2}{3}}}{- \frac{\sqrt[3]{21} \left(27 + 5 \sqrt{30}\right)^{\frac{2}{3}}}{3} + \frac{21^{\frac{2}{3}}}{3} + 7 \sqrt[3]{27 + 5 \sqrt{30}}} + \frac{3^{\frac{5}{6}} \sqrt[3]{7} \sqrt[3]{27 + 5 \sqrt{30}}}{15 \left(- \frac{\sqrt[3]{21} \sqrt[3]{27 + 5 \sqrt{30}}}{15} + \frac{21^{\frac{2}{3}}}{15 \sqrt[3]{27 + 5 \sqrt{30}}} + \frac{7}{5}\right)} \right)}}{2} \right)}\right)\right) \left(x + \left(- \sqrt[4]{- \frac{7 \sqrt{10} \cdot 3^{\frac{5}{6}} \sqrt[3]{7}}{5 \left(27 + 5 \sqrt{30}\right)^{\frac{2}{3}}} - \frac{539 \sqrt[3]{21}}{75 \left(27 + 5 \sqrt{30}\right)^{\frac{2}{3}}} + \frac{14 \cdot 21^{\frac{2}{3}}}{75 \sqrt[3]{27 + 5 \sqrt{30}}} + \frac{7 \sqrt[3]{21} \sqrt[3]{27 + 5 \sqrt{30}}}{75} + \frac{4 \cdot 21^{\frac{2}{3}} \left(27 + 5 \sqrt{30}\right)^{\frac{2}{3}}}{225} + \frac{7}{3}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt[6]{3} \cdot 7^{\frac{2}{3}}}{- \frac{\sqrt[3]{21} \left(27 + 5 \sqrt{30}\right)^{\frac{2}{3}}}{3} + \frac{21^{\frac{2}{3}}}{3} + 7 \sqrt[3]{27 + 5 \sqrt{30}}} + \frac{3^{\frac{5}{6}} \sqrt[3]{7} \sqrt[3]{27 + 5 \sqrt{30}}}{15 \left(- \frac{\sqrt[3]{21} \sqrt[3]{27 + 5 \sqrt{30}}}{15} + \frac{21^{\frac{2}{3}}}{15 \sqrt[3]{27 + 5 \sqrt{30}}} + \frac{7}{5}\right)} \right)}}{2} \right)} - i \sqrt[4]{- \frac{7 \sqrt{10} \cdot 3^{\frac{5}{6}} \sqrt[3]{7}}{5 \left(27 + 5 \sqrt{30}\right)^{\frac{2}{3}}} - \frac{539 \sqrt[3]{21}}{75 \left(27 + 5 \sqrt{30}\right)^{\frac{2}{3}}} + \frac{14 \cdot 21^{\frac{2}{3}}}{75 \sqrt[3]{27 + 5 \sqrt{30}}} + \frac{7 \sqrt[3]{21} \sqrt[3]{27 + 5 \sqrt{30}}}{75} + \frac{4 \cdot 21^{\frac{2}{3}} \left(27 + 5 \sqrt{30}\right)^{\frac{2}{3}}}{225} + \frac{7}{3}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt[6]{3} \cdot 7^{\frac{2}{3}}}{- \frac{\sqrt[3]{21} \left(27 + 5 \sqrt{30}\right)^{\frac{2}{3}}}{3} + \frac{21^{\frac{2}{3}}}{3} + 7 \sqrt[3]{27 + 5 \sqrt{30}}} + \frac{3^{\frac{5}{6}} \sqrt[3]{7} \sqrt[3]{27 + 5 \sqrt{30}}}{15 \left(- \frac{\sqrt[3]{21} \sqrt[3]{27 + 5 \sqrt{30}}}{15} + \frac{21^{\frac{2}{3}}}{15 \sqrt[3]{27 + 5 \sqrt{30}}} + \frac{7}{5}\right)} \right)}}{2} \right)}\right)\right)$$

Собрать выражение

            5    7
 3       3*x    x 
x  - x - ---- + --
          5     7 

$$\frac{x^{7}}{7} - \frac{3 x^{5}}{5} + x^{3} - x$$

Общее упрощение

            5    7
 3       3*x    x 
x  - x - ---- + --
          5     7 

$$\frac{x^{7}}{7} - \frac{3 x^{5}}{5} + x^{3} - x$$