Производная log((sqrt(x+1)+sqrt(x-1))/(sqrt(x+1)-sqrt(x-1)))-2*atan(sqrt((x-1)/(x+1)))

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                             /  _______     ________\ /    1             1     \     /    1           1     \  /  _______     ________\     /    1           1     \ /    1           1     \                                                                                                                                                                                                                                                                                                                                            
                             \\/ 1 + x  + \/ -1 + x /*|---------- - -----------|   2*|--------- - ----------| *\\/ 1 + x  + \/ -1 + x /   2*|--------- + ----------|*|--------- - ----------|                            /                         /  _______     ________\ /    1           1     \\                                                                                       /                         /  _______     ________\ /    1           1     \\                                                                 
                                                      |       3/2           3/2|     |  _______     ________|                               |  _______     ________| |  _______     ________|                            |                         \\/ 1 + x  + \/ -1 + x /*|--------- - ----------||                                                                                       |                         \\/ 1 + x  + \/ -1 + x /*|--------- - ----------||                                                                 
      1             1                                 \(1 + x)      (-1 + x)   /     \\/ 1 + x    \/ -1 + x /                               \\/ 1 + x    \/ -1 + x / \\/ 1 + x    \/ -1 + x /                            |                                                  |  _______     ________||                                                                                       |                                                  |  _______     ________||                                                                 
  ---------- + ----------- + --------------------------------------------------- - ---------------------------------------------------- - ---------------------------------------------------   /    1           1     \ |    1           1                                 \\/ 1 + x    \/ -1 + x /|       ________                     ________              2   /    1           1     \ |    1           1                                 \\/ 1 + x    \/ -1 + x /|        ________              2           ________               
         3/2           3/2                    ________     _______                                                      2                                  ________     _______                 |--------- + ----------|*|--------- + ---------- + -------------------------------------------------|      / -1 + x  /     -1 + x\      / -1 + x  /     -1 + x\    |--------- - ----------|*|--------- + ---------- + -------------------------------------------------|       / -1 + x  /     -1 + x\           / -1 + x  /     -1 + x\ 
  (1 + x)      (-1 + x)                     \/ -1 + x  - \/ 1 + x                               /  ________     _______\                                 \/ -1 + x  - \/ 1 + x                  |  _______     ________| |  _______     ________                   ________     _______             |     /  ------ *|-1 + ------|     /  ------ *|-1 + ------|    |  _______     ________| |  _______     ________                   ________     _______             |      /  ------ *|-1 + ------|          /  ------ *|-1 + ------| 
                                                                                                \\/ -1 + x  - \/ 1 + x /                                                                        \\/ 1 + x    \/ -1 + x / \\/ 1 + x    \/ -1 + x                  \/ -1 + x  - \/ 1 + x              /   \/   1 + x   \     1 + x /   \/   1 + x   \     1 + x /    \\/ 1 + x    \/ -1 + x / \\/ 1 + x    \/ -1 + x                  \/ -1 + x  - \/ 1 + x              /    \/   1 + x   \     1 + x /        \/   1 + x   \     1 + x / 
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                                                                                     /  _______     ________\                                                                                                                                                  2                                          /    -1 + x\         2         /    -1 + x\         2                               /  _______     ________\ /  ________     _______\                                                2                    /    -1 + x\         
                                                                                   4*\\/ 1 + x  + \/ -1 + x /                                                                                                                          /  _______     ________\                                           |1 + ------|*(-1 + x)        2*|1 + ------|*(-1 + x)                              4*\\/ 1 + x  + \/ -1 + x /*\\/ -1 + x  - \/ 1 + x /                                    /    -1 + x\             (1 + x)*|1 + ------|*(-1 + x)
                                                                                                                                                                                                                                     4*\\/ 1 + x  + \/ -1 + x /                                           \    1 + x /                   \    1 + x /                                                                                                                      (1 + x)*|1 + ------| *(-1 + x)           \    1 + x /         
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   \    1 + x /                                          

$$- \frac{\sqrt{\frac{x - 1}{x + 1}} \left(\frac{x - 1}{x + 1} - 1\right)^{2}}{2 \left(x - 1\right)^{2} \left(\frac{x - 1}{x + 1} + 1\right)} - \frac{\frac{\left(\sqrt{x - 1} + \sqrt{x + 1}\right) \left(\frac{1}{\left(x + 1\right)^{\frac{3}{2}}} - \frac{1}{\left(x - 1\right)^{\frac{3}{2}}}\right)}{\sqrt{x - 1} - \sqrt{x + 1}} - \frac{2 \cdot \left(\frac{1}{\sqrt{x + 1}} - \frac{1}{\sqrt{x - 1}}\right) \left(\frac{1}{\sqrt{x + 1}} + \frac{1}{\sqrt{x - 1}}\right)}{\sqrt{x - 1} - \sqrt{x + 1}} - \frac{2 \left(\sqrt{x - 1} + \sqrt{x + 1}\right) \left(\frac{1}{\sqrt{x + 1}} - \frac{1}{\sqrt{x - 1}}\right)^{2}}{\left(\sqrt{x - 1} - \sqrt{x + 1}\right)^{2}} + \frac{1}{\left(x + 1\right)^{\frac{3}{2}}} + \frac{1}{\left(x - 1\right)^{\frac{3}{2}}}}{4 \left(\sqrt{x - 1} + \sqrt{x + 1}\right)} - \frac{\left(\frac{1}{\sqrt{x + 1}} + \frac{1}{\sqrt{x - 1}}\right) \left(\frac{\left(\sqrt{x - 1} + \sqrt{x + 1}\right) \left(\frac{1}{\sqrt{x + 1}} - \frac{1}{\sqrt{x - 1}}\right)}{\sqrt{x - 1} - \sqrt{x + 1}} + \frac{1}{\sqrt{x + 1}} + \frac{1}{\sqrt{x - 1}}\right)}{4 \left(\sqrt{x - 1} + \sqrt{x + 1}\right)^{2}} - \frac{\left(\frac{1}{\sqrt{x + 1}} - \frac{1}{\sqrt{x - 1}}\right) \left(\frac{\left(\sqrt{x - 1} + \sqrt{x + 1}\right) \left(\frac{1}{\sqrt{x + 1}} - \frac{1}{\sqrt{x - 1}}\right)}{\sqrt{x - 1} - \sqrt{x + 1}} + \frac{1}{\sqrt{x + 1}} + \frac{1}{\sqrt{x - 1}}\right)}{4 \left(\sqrt{x - 1} - \sqrt{x + 1}\right) \left(\sqrt{x - 1} + \sqrt{x + 1}\right)} + \frac{\sqrt{\frac{x - 1}{x + 1}} \left(\frac{x - 1}{x + 1} - 1\right)^{2}}{\left(x - 1\right) \left(x + 1\right) \left(\frac{x - 1}{x + 1} + 1\right)^{2}} - \frac{\sqrt{\frac{x - 1}{x + 1}} \left(\frac{x - 1}{x + 1} - 1\right)}{\left(x - 1\right) \left(x + 1\right) \left(\frac{x - 1}{x + 1} + 1\right)} - \frac{\sqrt{\frac{x - 1}{x + 1}} \left(\frac{x - 1}{x + 1} - 1\right)}{\left(x - 1\right)^{2} \left(\frac{x - 1}{x + 1} + 1\right)}$$

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  |                           /  _______     ________\ /    1             1     \   /    1             1     \ /    1           1     \   /    1             1     \ /    1           1     \     /    1           1     \  /    1           1     \     /    1           1     \  /  _______     ________\     /  _______     ________\ /    1             1     \ /    1           1     \|                                                                                                                                     |                           /  _______     ________\ /    1             1     \     /    1           1     \  /  _______     ________\     /    1           1     \ /    1           1     \|                                                                                                                                                                                                   |                           /  _______     ________\ /    1             1     \     /    1           1     \  /  _______     ________\     /    1           1     \ /    1           1     \|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        
  |                           \\/ 1 + x  + \/ -1 + x /*|---------- - -----------|   |---------- + -----------|*|--------- - ----------|   |---------- - -----------|*|--------- + ----------|   2*|--------- - ----------| *|--------- + ----------|   2*|--------- - ----------| *\\/ 1 + x  + \/ -1 + x /   2*\\/ 1 + x  + \/ -1 + x /*|---------- - -----------|*|--------- - ----------||                             /                         /  _______     ________\ /    1           1     \\                            |                           \\/ 1 + x  + \/ -1 + x /*|---------- - -----------|   2*|--------- - ----------| *\\/ 1 + x  + \/ -1 + x /   2*|--------- + ----------|*|--------- - ----------||                              /                         /  _______     ________\ /    1           1     \\                                                                                         |                           \\/ 1 + x  + \/ -1 + x /*|---------- - -----------|   2*|--------- - ----------| *\\/ 1 + x  + \/ -1 + x /   2*|--------- + ----------|*|--------- - ----------||                              /                         /  _______     ________\ /    1           1     \\                                                                                                                                                                                                                                                                                               /                         /  _______     ________\ /    1           1     \\                                   
  |                                                    |       5/2           5/2|   |       3/2           3/2| |  _______     ________|   |       3/2           3/2| |  _______     ________|     |  _______     ________|  |  _______     ________|     |  _______     ________|                                                        |       3/2           3/2| |  _______     ________||                             |                         \\/ 1 + x  + \/ -1 + x /*|--------- - ----------||                            |                                                    |       3/2           3/2|     |  _______     ________|                               |  _______     ________| |  _______     ________||                              |                         \\/ 1 + x  + \/ -1 + x /*|--------- - ----------||                                                                                         |                                                    |       3/2           3/2|     |  _______     ________|                               |  _______     ________| |  _______     ________||                              |                         \\/ 1 + x  + \/ -1 + x /*|--------- - ----------||                                                                                                                                                                                                                                                                                               |                         \\/ 1 + x  + \/ -1 + x /*|--------- - ----------||                                   
  |    1             1                                 \(1 + x)      (-1 + x)   /   \(1 + x)      (-1 + x)   / \\/ 1 + x    \/ -1 + x /   \(1 + x)      (-1 + x)   / \\/ 1 + x    \/ -1 + x /     \\/ 1 + x    \/ -1 + x /  \\/ 1 + x    \/ -1 + x /     \\/ 1 + x    \/ -1 + x /                                                        \(1 + x)      (-1 + x)   / \\/ 1 + x    \/ -1 + x /|                           2 |                                                  |  _______     ________||   /    1           1     \ |    1             1                                 \(1 + x)      (-1 + x)   /     \\/ 1 + x    \/ -1 + x /                               \\/ 1 + x    \/ -1 + x / \\/ 1 + x    \/ -1 + x /|                              |                                                  |  _______     ________||                                                                /    1           1     \ |    1             1                                 \(1 + x)      (-1 + x)   /     \\/ 1 + x    \/ -1 + x /                               \\/ 1 + x    \/ -1 + x / \\/ 1 + x    \/ -1 + x /|                              |                                                  |  _______     ________||                                                                                                                                                                                                                                                                                               |                                                  |  _______     ________||                                   
3*|---------- + ----------- + --------------------------------------------------- - --------------------------------------------------- - --------------------------------------------------- + ---------------------------------------------------- + ---------------------------------------------------- - ------------------------------------------------------------------------------|   /    1           1     \  |    1           1                                 \\/ 1 + x    \/ -1 + x /|   |--------- + ----------|*|---------- + ----------- + --------------------------------------------------- - ---------------------------------------------------- - ---------------------------------------------------|   /    1             1     \ |    1           1                                 \\/ 1 + x    \/ -1 + x /|         ________                     ________              3   |--------- - ----------|*|---------- + ----------- + --------------------------------------------------- - ---------------------------------------------------- - ---------------------------------------------------|   /    1             1     \ |    1           1                                 \\/ 1 + x    \/ -1 + x /|         ________              2         ________              3            ________              2           ________              2           ________                         ________                         ________              3    /    1           1     \ /    1           1     \ |    1           1                                 \\/ 1 + x    \/ -1 + x /|          ________              2  
  |       5/2           5/2                    ________     _______                                  ________     _______                                  ________     _______                                                      2                                                      3                                                                   2                           |   |--------- + ----------| *|--------- + ---------- + -------------------------------------------------|   |  _______     ________| |       3/2           3/2                    ________     _______                                                      2                                  ________     _______              |   |---------- + -----------|*|--------- + ---------- + -------------------------------------------------|        / -1 + x  /     -1 + x\      / -1 + x  /     -1 + x\    |  _______     ________| |       3/2           3/2                    ________     _______                                                      2                                  ________     _______              |   |---------- - -----------|*|--------- + ---------- + -------------------------------------------------|        / -1 + x  /     -1 + x\         / -1 + x  /     -1 + x\            / -1 + x  /     -1 + x\           / -1 + x  /     -1 + x\           / -1 + x  /     -1 + x\          / -1 + x  /     -1 + x\          / -1 + x  /     -1 + x\     |--------- + ----------|*|--------- - ----------|*|--------- + ---------- + -------------------------------------------------|         / -1 + x  /     -1 + x\   
  |(1 + x)      (-1 + x)                     \/ -1 + x  - \/ 1 + x                                 \/ -1 + x  - \/ 1 + x                                 \/ -1 + x  - \/ 1 + x                               /  ________     _______\                               /  ________     _______\                                            /  ________     _______\                            |   |  _______     ________|  |  _______     ________                   ________     _______             |   \\/ 1 + x    \/ -1 + x / |(1 + x)      (-1 + x)                     \/ -1 + x  - \/ 1 + x                               /  ________     _______\                                 \/ -1 + x  - \/ 1 + x               |   |       3/2           3/2| |  _______     ________                   ________     _______             |   2*  /  ------ *|-1 + ------|     /  ------ *|-1 + ------|    \\/ 1 + x    \/ -1 + x / |(1 + x)      (-1 + x)                     \/ -1 + x  - \/ 1 + x                               /  ________     _______\                                 \/ -1 + x  - \/ 1 + x               |   |       3/2           3/2| |  _______     ________                   ________     _______             |   3*  /  ------ *|-1 + ------|        /  ------ *|-1 + ------|       4*  /  ------ *|-1 + ------|      2*  /  ------ *|-1 + ------|      2*  /  ------ *|-1 + ------|     2*  /  ------ *|-1 + ------|     2*  /  ------ *|-1 + ------|     |  _______     ________| |  _______     ________| |  _______     ________                   ________     _______             |    3*  /  ------ *|-1 + ------|   
  \                                                                                                                                                                                                          \\/ -1 + x  - \/ 1 + x /                               \\/ -1 + x  - \/ 1 + x /                                            \\/ -1 + x  - \/ 1 + x /                            /   \\/ 1 + x    \/ -1 + x /  \\/ 1 + x    \/ -1 + x                  \/ -1 + x  - \/ 1 + x              /                            \                                                                                              \\/ -1 + x  - \/ 1 + x /                                                                     /   \(1 + x)      (-1 + x)   / \\/ 1 + x    \/ -1 + x                  \/ -1 + x  - \/ 1 + x              /     \/   1 + x   \     1 + x /   \/   1 + x   \     1 + x /                             \                                                                                              \\/ -1 + x  - \/ 1 + x /                                                                     /   \(1 + x)      (-1 + x)   / \\/ 1 + x    \/ -1 + x                  \/ -1 + x  - \/ 1 + x              /     \/   1 + x   \     1 + x /      \/   1 + x   \     1 + x /         \/   1 + x   \     1 + x /        \/   1 + x   \     1 + x /        \/   1 + x   \     1 + x /       \/   1 + x   \     1 + x /       \/   1 + x   \     1 + x /     \\/ 1 + x    \/ -1 + x / \\/ 1 + x    \/ -1 + x / \\/ 1 + x    \/ -1 + x                  \/ -1 + x  - \/ 1 + x              /      \/   1 + x   \     1 + x /   
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                                                                                                                                                                                    /  _______     ________\                                                                                                                                                                                                                                                   3                                                                                                                                                                2                                                                                                                                                                 2                                            /    -1 + x\         3          /    -1 + x\         3                                                                                       /  _______     ________\ /  ________     _______\                                                                                                                 /  _______     ________\ /  ________     _______\                                  /    -1 + x\         3                         2                                  2                                2                     /    -1 + x\         2          2 /    -1 + x\                                 3                                                                           2                                                                           /    -1 + x\         2
                                                                                                                                                                                  8*\\/ 1 + x  + \/ -1 + x /                                                                                                                                                                                                                           /  _______     ________\                                                                                                                                         /  _______     ________\                                                                                                                                          /  _______     ________\                                             |1 + ------|*(-1 + x)         4*|1 + ------|*(-1 + x)                                                                                      4*\\/ 1 + x  + \/ -1 + x /*\\/ -1 + x  - \/ 1 + x /                                                                                                               8*\\/ 1 + x  + \/ -1 + x /*\\/ -1 + x  - \/ 1 + x /                                2*|1 + ------|*(-1 + x)              /    -1 + x\          2          2 /    -1 + x\                     /    -1 + x\          2   (1 + x)*|1 + ------|*(-1 + x)    (1 + x) *|1 + ------|*(-1 + x)          2 /    -1 + x\                                                    /  _______     ________\  /  ________     _______\                                        2*(1 + x)*|1 + ------|*(-1 + x) 
                                                                                                                                                                                                                                                                                                                                                                                                                                     4*\\/ 1 + x  + \/ -1 + x /                                                                                                                                       4*\\/ 1 + x  + \/ -1 + x /                                                                                                                                        8*\\/ 1 + x  + \/ -1 + x /                                             \    1 + x /                    \    1 + x /                                                                                                                                                                                                                                                                                                                                                      \    1 + x /               (1 + x)*|1 + ------| *(-1 + x)    (1 + x) *|1 + ------| *(-1 + x)   (1 + x)*|1 + ------| *(-1 + x)            \    1 + x /                      \    1 + x /            (1 + x) *|1 + ------| *(-1 + x)                                        4*\\/ 1 + x  + \/ -1 + x / *\\/ -1 + x  - \/ 1 + x /                                                  \    1 + x /          
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    \    1 + x /                       \    1 + x /                     \    1 + x /                                                                                         \    1 + x /                                                                                                                                                                              

$$\frac{\sqrt{\frac{x - 1}{x + 1}} \left(\frac{x - 1}{x + 1} - 1\right)^{3}}{4 \left(x - 1\right)^{3} \left(\frac{x - 1}{x + 1} + 1\right)} + \frac{3 \left(\frac{\left(\sqrt{x - 1} + \sqrt{x + 1}\right) \left(\frac{1}{\left(x + 1\right)^{\frac{5}{2}}} - \frac{1}{\left(x - 1\right)^{\frac{5}{2}}}\right)}{\sqrt{x - 1} - \sqrt{x + 1}} - \frac{\left(\frac{1}{\left(x + 1\right)^{\frac{3}{2}}} - \frac{1}{\left(x - 1\right)^{\frac{3}{2}}}\right) \left(\frac{1}{\sqrt{x + 1}} + \frac{1}{\sqrt{x - 1}}\right)}{\sqrt{x - 1} - \sqrt{x + 1}} - \frac{\left(\frac{1}{\left(x + 1\right)^{\frac{3}{2}}} + \frac{1}{\left(x - 1\right)^{\frac{3}{2}}}\right) \left(\frac{1}{\sqrt{x + 1}} - \frac{1}{\sqrt{x - 1}}\right)}{\sqrt{x - 1} - \sqrt{x + 1}} - \frac{2 \left(\sqrt{x - 1} + \sqrt{x + 1}\right) \left(\frac{1}{\left(x + 1\right)^{\frac{3}{2}}} - \frac{1}{\left(x - 1\right)^{\frac{3}{2}}}\right) \left(\frac{1}{\sqrt{x + 1}} - \frac{1}{\sqrt{x - 1}}\right)}{\left(\sqrt{x - 1} - \sqrt{x + 1}\right)^{2}} + \frac{2 \left(\frac{1}{\sqrt{x + 1}} - \frac{1}{\sqrt{x - 1}}\right)^{2} \cdot \left(\frac{1}{\sqrt{x + 1}} + \frac{1}{\sqrt{x - 1}}\right)}{\left(\sqrt{x - 1} - \sqrt{x + 1}\right)^{2}} + \frac{2 \left(\sqrt{x - 1} + \sqrt{x + 1}\right) \left(\frac{1}{\sqrt{x + 1}} - \frac{1}{\sqrt{x - 1}}\right)^{3}}{\left(\sqrt{x - 1} - \sqrt{x + 1}\right)^{3}} + \frac{1}{\left(x + 1\right)^{\frac{5}{2}}} + \frac{1}{\left(x - 1\right)^{\frac{5}{2}}}\right)}{8 \left(\sqrt{x - 1} + \sqrt{x + 1}\right)} + \frac{\left(\frac{1}{\left(x + 1\right)^{\frac{3}{2}}} + \frac{1}{\left(x - 1\right)^{\frac{3}{2}}}\right) \left(\frac{\left(\sqrt{x - 1} + \sqrt{x + 1}\right) \left(\frac{1}{\sqrt{x + 1}} - \frac{1}{\sqrt{x - 1}}\right)}{\sqrt{x - 1} - \sqrt{x + 1}} + \frac{1}{\sqrt{x + 1}} + \frac{1}{\sqrt{x - 1}}\right)}{8 \left(\sqrt{x - 1} + \sqrt{x + 1}\right)^{2}} + \frac{\left(\frac{1}{\sqrt{x + 1}} + \frac{1}{\sqrt{x - 1}}\right) \left(\frac{\left(\sqrt{x - 1} + \sqrt{x + 1}\right) \left(\frac{1}{\left(x + 1\right)^{\frac{3}{2}}} - \frac{1}{\left(x - 1\right)^{\frac{3}{2}}}\right)}{\sqrt{x - 1} - \sqrt{x + 1}} - \frac{2 \cdot \left(\frac{1}{\sqrt{x + 1}} - \frac{1}{\sqrt{x - 1}}\right) \left(\frac{1}{\sqrt{x + 1}} + \frac{1}{\sqrt{x - 1}}\right)}{\sqrt{x - 1} - \sqrt{x + 1}} - \frac{2 \left(\sqrt{x - 1} + \sqrt{x + 1}\right) \left(\frac{1}{\sqrt{x + 1}} - \frac{1}{\sqrt{x - 1}}\right)^{2}}{\left(\sqrt{x - 1} - \sqrt{x + 1}\right)^{2}} + \frac{1}{\left(x + 1\right)^{\frac{3}{2}}} + \frac{1}{\left(x - 1\right)^{\frac{3}{2}}}\right)}{4 \left(\sqrt{x - 1} + \sqrt{x + 1}\right)^{2}} + \frac{\left(\frac{1}{\sqrt{x + 1}} + \frac{1}{\sqrt{x - 1}}\right)^{2} \left(\frac{\left(\sqrt{x - 1} + \sqrt{x + 1}\right) \left(\frac{1}{\sqrt{x + 1}} - \frac{1}{\sqrt{x - 1}}\right)}{\sqrt{x - 1} - \sqrt{x + 1}} + \frac{1}{\sqrt{x + 1}} + \frac{1}{\sqrt{x - 1}}\right)}{4 \left(\sqrt{x - 1} + \sqrt{x + 1}\right)^{3}} + \frac{\left(\frac{1}{\left(x + 1\right)^{\frac{3}{2}}} - \frac{1}{\left(x - 1\right)^{\frac{3}{2}}}\right) \left(\frac{\left(\sqrt{x - 1} + \sqrt{x + 1}\right) \left(\frac{1}{\sqrt{x + 1}} - \frac{1}{\sqrt{x - 1}}\right)}{\sqrt{x - 1} - \sqrt{x + 1}} + \frac{1}{\sqrt{x + 1}} + \frac{1}{\sqrt{x - 1}}\right)}{8 \left(\sqrt{x - 1} - \sqrt{x + 1}\right) \left(\sqrt{x - 1} + \sqrt{x + 1}\right)} + \frac{\left(\frac{1}{\sqrt{x + 1}} - \frac{1}{\sqrt{x - 1}}\right) \left(\frac{\left(\sqrt{x - 1} + \sqrt{x + 1}\right) \left(\frac{1}{\left(x + 1\right)^{\frac{3}{2}}} - \frac{1}{\left(x - 1\right)^{\frac{3}{2}}}\right)}{\sqrt{x - 1} - \sqrt{x + 1}} - \frac{2 \cdot \left(\frac{1}{\sqrt{x + 1}} - \frac{1}{\sqrt{x - 1}}\right) \left(\frac{1}{\sqrt{x + 1}} + \frac{1}{\sqrt{x - 1}}\right)}{\sqrt{x - 1} - \sqrt{x + 1}} - \frac{2 \left(\sqrt{x - 1} + \sqrt{x + 1}\right) \left(\frac{1}{\sqrt{x + 1}} - \frac{1}{\sqrt{x - 1}}\right)^{2}}{\left(\sqrt{x - 1} - \sqrt{x + 1}\right)^{2}} + \frac{1}{\left(x + 1\right)^{\frac{3}{2}}} + \frac{1}{\left(x - 1\right)^{\frac{3}{2}}}\right)}{4 \left(\sqrt{x - 1} - \sqrt{x + 1}\right) \left(\sqrt{x - 1} + \sqrt{x + 1}\right)} + \frac{\left(\frac{1}{\sqrt{x + 1}} - \frac{1}{\sqrt{x - 1}}\right) \left(\frac{1}{\sqrt{x + 1}} + \frac{1}{\sqrt{x - 1}}\right) \left(\frac{\left(\sqrt{x - 1} + \sqrt{x + 1}\right) \left(\frac{1}{\sqrt{x + 1}} - \frac{1}{\sqrt{x - 1}}\right)}{\sqrt{x - 1} - \sqrt{x + 1}} + \frac{1}{\sqrt{x + 1}} + \frac{1}{\sqrt{x - 1}}\right)}{4 \left(\sqrt{x - 1} - \sqrt{x + 1}\right) \left(\sqrt{x - 1} + \sqrt{x + 1}\right)^{2}} - \frac{\sqrt{\frac{x - 1}{x + 1}} \left(\frac{x - 1}{x + 1} - 1\right)^{3}}{\left(x - 1\right)^{2} \left(x + 1\right) \left(\frac{x - 1}{x + 1} + 1\right)^{2}} + \frac{3 \sqrt{\frac{x - 1}{x + 1}} \left(\frac{x - 1}{x + 1} - 1\right)^{2}}{2 \left(x - 1\right)^{2} \left(x + 1\right) \left(\frac{x - 1}{x + 1} + 1\right)} + \frac{3 \sqrt{\frac{x - 1}{x + 1}} \left(\frac{x - 1}{x + 1} - 1\right)^{2}}{2 \left(x - 1\right)^{3} \left(\frac{x - 1}{x + 1} + 1\right)} + \frac{2 \sqrt{\frac{x - 1}{x + 1}} \left(\frac{x - 1}{x + 1} - 1\right)^{3}}{\left(x - 1\right) \left(x + 1\right)^{2} \left(\frac{x - 1}{x + 1} + 1\right)^{3}} - \frac{4 \sqrt{\frac{x - 1}{x + 1}} \left(\frac{x - 1}{x + 1} - 1\right)^{2}}{\left(x - 1\right) \left(x + 1\right)^{2} \left(\frac{x - 1}{x + 1} + 1\right)^{2}} + \frac{2 \sqrt{\frac{x - 1}{x + 1}} \left(\frac{x - 1}{x + 1} - 1\right)}{\left(x - 1\right) \left(x + 1\right)^{2} \left(\frac{x - 1}{x + 1} + 1\right)} - \frac{2 \sqrt{\frac{x - 1}{x + 1}} \left(\frac{x - 1}{x + 1} - 1\right)^{2}}{\left(x - 1\right)^{2} \left(x + 1\right) \left(\frac{x - 1}{x + 1} + 1\right)^{2}} + \frac{2 \sqrt{\frac{x - 1}{x + 1}} \left(\frac{x - 1}{x + 1} - 1\right)}{\left(x - 1\right)^{2} \left(x + 1\right) \left(\frac{x - 1}{x + 1} + 1\right)} + \frac{2 \sqrt{\frac{x - 1}{x + 1}} \left(\frac{x - 1}{x + 1} - 1\right)}{\left(x - 1\right)^{3} \left(\frac{x - 1}{x + 1} + 1\right)}$$

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