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Общий знаменатель log(((2*sin(x))/(1+cos(x) ... (x))/(1+cos(x))))/sqrt(2)

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Примеры

Решение

Вы ввели [src]
   / 2*sin(x)     3/2    \
   |---------- - 2    + 2|
   |1 + cos(x)           |
log|---------------------|
   |     3/2    2*sin(x) |
   |2 + 2    + ----------|
   \           1 + cos(x)/
--------------------------
            ___           
          \/ 2
$$\frac{1}{\sqrt{2}} \log{\left (\frac{- 2 \sqrt{2} + \frac{2 \sin{\left (x \right )}}{\cos{\left (x \right )} + 1} + 2}{2 + 2^{\frac{3}{2}} + \frac{2 \sin{\left (x \right )}}{\cos{\left (x \right )} + 1}} \right )}$$
Степени [src]
         /        ___    2*sin(x) \
         |2 - 2*\/ 2  + ----------|
  ___    |              1 + cos(x)|
\/ 2 *log|------------------------|
         |        ___    2*sin(x) |
         |2 + 2*\/ 2  + ----------|
         \              1 + cos(x)/
-----------------------------------
                 2
$$\frac{\sqrt{2}}{2} \log{\left (\frac{- 2 \sqrt{2} + 2 + \frac{2 \sin{\left (x \right )}}{\cos{\left (x \right )} + 1}}{2 + 2 \sqrt{2} + \frac{2 \sin{\left (x \right )}}{\cos{\left (x \right )} + 1}} \right )}$$
Численный ответ [src]
0.707106781186547*log(((2*sin(x))/(1 + cos(x)) - 2^(3/2) + 2)/(2 + 2^(3/2) + (2*sin(x))/(1 + cos(x))))
Рациональный знаменатель [src]
         /  /     3/2              /     3/2    2*sin(x) \            ___ /     3/2                  ___           2*sin(x)    2*cos(x)*sin(x)\       ___           2*sin(x)    2*cos(x)*sin(x)\\
         |2*|2 + 2    + 2*cos(x) + |2 + 2    + ----------|*sin(x) - \/ 2 *|2 + 2    + 2*cos(x) + 2*\/ 2 *cos(x) + ---------- + ---------------| + 2*\/ 2 *cos(x) + ---------- + ---------------||
  ___    |  \                      \           1 + cos(x)/                \                                       1 + cos(x)      1 + cos(x)  /                    1 + cos(x)      1 + cos(x)  /|
\/ 2 *log|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
         |                                            /     3/2    2*sin(x) \ /     3/2                  ___           2*sin(x)    2*cos(x)*sin(x)\                                             |
         |                                            |2 + 2    + ----------|*|2 + 2    + 2*cos(x) + 2*\/ 2 *cos(x) + ---------- + ---------------|                                             |
         \                                            \           1 + cos(x)/ \                                       1 + cos(x)      1 + cos(x)  /                                             /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                2
$$\frac{\sqrt{2}}{2} \log{\left (\frac{2 \left(2 + 2^{\frac{3}{2}} + \frac{2 \sin{\left (x \right )}}{\cos{\left (x \right )} + 1}\right) \sin{\left (x \right )} - 2 \sqrt{2} \left(2 \cos{\left (x \right )} + 2 \sqrt{2} \cos{\left (x \right )} + 2 + 2^{\frac{3}{2}} + \frac{2 \sin{\left (x \right )} \cos{\left (x \right )}}{\cos{\left (x \right )} + 1} + \frac{2 \sin{\left (x \right )}}{\cos{\left (x \right )} + 1}\right) + 4 \cos{\left (x \right )} + 4 \sqrt{2} \cos{\left (x \right )} + 4 + 4 \sqrt{2} + \frac{4 \sin{\left (x \right )} \cos{\left (x \right )}}{\cos{\left (x \right )} + 1} + \frac{4 \sin{\left (x \right )}}{\cos{\left (x \right )} + 1}}{\left(2 + 2^{\frac{3}{2}} + \frac{2 \sin{\left (x \right )}}{\cos{\left (x \right )} + 1}\right) \left(2 \cos{\left (x \right )} + 2 \sqrt{2} \cos{\left (x \right )} + 2 + 2^{\frac{3}{2}} + \frac{2 \sin{\left (x \right )} \cos{\left (x \right )}}{\cos{\left (x \right )} + 1} + \frac{2 \sin{\left (x \right )}}{\cos{\left (x \right )} + 1}\right)} \right )}$$
Объединение рациональных выражений [src]
         /      ___                               \
  ___    |1 - \/ 2 *(1 + cos(x)) + cos(x) + sin(x)|
\/ 2 *log|----------------------------------------|
         |   /      ___\                          |
         \   \1 + \/ 2 /*(1 + cos(x)) + sin(x)    /
---------------------------------------------------
                         2
$$\frac{\sqrt{2}}{2} \log{\left (\frac{- \sqrt{2} \left(\cos{\left (x \right )} + 1\right) + \sin{\left (x \right )} + \cos{\left (x \right )} + 1}{\left(1 + \sqrt{2}\right) \left(\cos{\left (x \right )} + 1\right) + \sin{\left (x \right )}} \right )}$$
Общее упрощение [src]
         /      ___     ___    /    pi\     ___       \
         |1 - \/ 2  + \/ 2 *sin|x + --| - \/ 2 *cos(x)|
  ___    |                     \    4 /               |
\/ 2 *log|--------------------------------------------|
         |     /      ___\                            |
         \     \1 + \/ 2 /*(1 + cos(x)) + sin(x)      /
-------------------------------------------------------
                           2
$$\frac{\sqrt{2}}{2} \log{\left (\frac{\sqrt{2} \sin{\left (x + \frac{\pi}{4} \right )} - \sqrt{2} \cos{\left (x \right )} - \sqrt{2} + 1}{\left(1 + \sqrt{2}\right) \left(\cos{\left (x \right )} + 1\right) + \sin{\left (x \right )}} \right )}$$
Собрать выражение [src]
         / 2*sin(x)     3/2    \
         |---------- - 2    + 2|
  ___    |1 + cos(x)           |
\/ 2 *log|---------------------|
         |     3/2    2*sin(x) |
         |2 + 2    + ----------|
         \           1 + cos(x)/
--------------------------------
               2
$$\frac{\sqrt{2}}{2} \log{\left (\frac{- 2 \sqrt{2} + \frac{2 \sin{\left (x \right )}}{\cos{\left (x \right )} + 1} + 2}{2 + 2^{\frac{3}{2}} + \frac{2 \sin{\left (x \right )}}{\cos{\left (x \right )} + 1}} \right )}$$
         /        ___              /        ___\       \
  ___    |2 - 2*\/ 2  + 2*sin(x) + \2 - 2*\/ 2 /*cos(x)|
\/ 2 *log|---------------------------------------------|
         |        ___              /        ___\       |
         \2 + 2*\/ 2  + 2*sin(x) + \2 + 2*\/ 2 /*cos(x)/
--------------------------------------------------------
                           2
$$\frac{\sqrt{2}}{2} \log{\left (\frac{2 \sin{\left (x \right )} + \left(- 2 \sqrt{2} + 2\right) \cos{\left (x \right )} - 2 \sqrt{2} + 2}{2 \sin{\left (x \right )} + \left(2 + 2 \sqrt{2}\right) \cos{\left (x \right )} + 2 + 2 \sqrt{2}} \right )}$$
Комбинаторика [src]
         /                                       ___                                                                                  \
  ___    |           2                       2*\/ 2                                            2*sin(x)                               |
\/ 2 *log|------------------------ - ------------------------ + ----------------------------------------------------------------------|
         |        ___    2*sin(x)            ___    2*sin(x)            ___                  ___           2*sin(x)    2*cos(x)*sin(x)|
         |2 + 2*\/ 2  + ----------   2 + 2*\/ 2  + ----------   2 + 2*\/ 2  + 2*cos(x) + 2*\/ 2 *cos(x) + ---------- + ---------------|
         \              1 + cos(x)                 1 + cos(x)                                             1 + cos(x)      1 + cos(x)  /
---------------------------------------------------------------------------------------------------------------------------------------
                                                                   2
$$\frac{\sqrt{2}}{2} \log{\left (\frac{2 \sin{\left (x \right )}}{2 \cos{\left (x \right )} + 2 \sqrt{2} \cos{\left (x \right )} + 2 + 2 \sqrt{2} + \frac{2 \sin{\left (x \right )} \cos{\left (x \right )}}{\cos{\left (x \right )} + 1} + \frac{2 \sin{\left (x \right )}}{\cos{\left (x \right )} + 1}} - \frac{2 \sqrt{2}}{2 + 2 \sqrt{2} + \frac{2 \sin{\left (x \right )}}{\cos{\left (x \right )} + 1}} + \frac{2}{2 + 2 \sqrt{2} + \frac{2 \sin{\left (x \right )}}{\cos{\left (x \right )} + 1}} \right )}$$
Общий знаменатель [src]
         /                                                                                                    ___         \
  ___    |          1                                          sin(x)                                       \/ 2          |
\/ 2 *log|---------------------- + -------------------------------------------------------------- - ----------------------|
         |      ___     sin(x)           ___     ___            sin(x)     cos(x)*sin(x)                  ___     sin(x)  |
         |1 + \/ 2  + ----------   1 + \/ 2  + \/ 2 *cos(x) + ---------- + ------------- + cos(x)   1 + \/ 2  + ----------|
         \            1 + cos(x)                              1 + cos(x)     1 + cos(x)                         1 + cos(x)/
---------------------------------------------------------------------------------------------------------------------------
                                                             2
$$\frac{\sqrt{2}}{2} \log{\left (\frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + \sqrt{2} \cos{\left (x \right )} + 1 + \sqrt{2} + \frac{\sin{\left (x \right )} \cos{\left (x \right )}}{\cos{\left (x \right )} + 1} + \frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1}} - \frac{\sqrt{2}}{1 + \sqrt{2} + \frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1}} + \frac{1}{1 + \sqrt{2} + \frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1}} \right )}$$
Тригонометрическая часть [src]
         /        ___    2*sin(x) \
         |2 - 2*\/ 2  + ----------|
  ___    |              1 + cos(x)|
\/ 2 *log|------------------------|
         |      3/2    2*sin(x)   |
         | 2 + 2    + ----------  |
         \            1 + cos(x)  /
-----------------------------------
                 2
$$\frac{\sqrt{2}}{2} \log{\left (\frac{- 2 \sqrt{2} + 2 + \frac{2 \sin{\left (x \right )}}{\cos{\left (x \right )} + 1}}{2 + 2^{\frac{3}{2}} + \frac{2 \sin{\left (x \right )}}{\cos{\left (x \right )} + 1}} \right )}$$
Раскрыть выражение [src]
         /        ___    2*sin(x) \
         |2 - 2*\/ 2  + ----------|
  ___    |              1 + cos(x)|
\/ 2 *log|------------------------|
         |        ___    2*sin(x) |
         |2 + 2*\/ 2  + ----------|
         \              1 + cos(x)/
-----------------------------------
                 2
$$\frac{\sqrt{2}}{2} \log{\left (\frac{- 2 \sqrt{2} + 2 + \frac{2 \sin{\left (x \right )}}{\cos{\left (x \right )} + 1}}{2 + 2 \sqrt{2} + \frac{2 \sin{\left (x \right )}}{\cos{\left (x \right )} + 1}} \right )}$$
  ___ /     /        ___    2*sin(x) \      /        ___    2*sin(x) \\
\/ 2 *|- log|2 + 2*\/ 2  + ----------| + log|2 - 2*\/ 2  + ----------||
      \     \              1 + cos(x)/      \              1 + cos(x)//
-----------------------------------------------------------------------
                                   2
$$\frac{\sqrt{2}}{2} \left(- \log{\left (2 + 2 \sqrt{2} + \frac{2 \sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )} + \log{\left (- 2 \sqrt{2} + 2 + \frac{2 \sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )}\right)$$