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Общий знаменатель 4*(log(sin(x)/(1+cos(x))+ ... 4+(4*sin(x))/(1+cos(x))))

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Примеры

Решение

Вы ввели [src]
  /   /  sin(x)      \                 \
  |log|---------- + 1|                 |
  |   \1 + cos(x)    /         1       |
4*|------------------- + --------------|
  |         4                 4*sin(x) |
  |                      4 + ----------|
  \                          1 + cos(x)/
$$4 \left(\frac{1}{4} \log{\left (1 + \frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )} + \frac{1}{4 + \frac{4 \sin{\left (x \right )}}{\cos{\left (x \right )} + 1}}\right)$$
Степени [src]
      4             /      sin(x)  \
-------------- + log|1 + ----------|
     4*sin(x)       \    1 + cos(x)/
4 + ----------                      
    1 + cos(x)
$$\log{\left (1 + \frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )} + \frac{4}{4 + \frac{4 \sin{\left (x \right )}}{\cos{\left (x \right )} + 1}}$$
Численный ответ [src]
1.0*log(sin(x)/(1 + cos(x)) + 1) + 4.0/(4.0 + 4.0*sin(x)/(1.0 + cos(x)))
Рациональный знаменатель [src]
              /      sin(x)  \      /      sin(x)  \                      /      sin(x)  \
1 + cos(x)*log|1 + ----------| + log|1 + ----------|*sin(x) + cos(x) + log|1 + ----------|
              \    1 + cos(x)/      \    1 + cos(x)/                      \    1 + cos(x)/
------------------------------------------------------------------------------------------
                                   1 + cos(x) + sin(x)
$$\frac{1}{\sin{\left (x \right )} + \cos{\left (x \right )} + 1} \left(\log{\left (1 + \frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )} \sin{\left (x \right )} + \log{\left (1 + \frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )} \cos{\left (x \right )} + \log{\left (1 + \frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )} + \cos{\left (x \right )} + 1\right)$$
Объединение рациональных выражений [src]
                             /1 + cos(x) + sin(x)\         
1 + (1 + cos(x) + sin(x))*log|-------------------| + cos(x)
                             \     1 + cos(x)    /         
-----------------------------------------------------------
                    1 + cos(x) + sin(x)
$$\frac{1}{\sin{\left (x \right )} + \cos{\left (x \right )} + 1} \left(\left(\sin{\left (x \right )} + \cos{\left (x \right )} + 1\right) \log{\left (\frac{\sin{\left (x \right )} + \cos{\left (x \right )} + 1}{\cos{\left (x \right )} + 1} \right )} + \cos{\left (x \right )} + 1\right)$$
Общее упрощение [src]
      4             /  sin(x)      \
-------------- + log|---------- + 1|
     4*sin(x)       \1 + cos(x)    /
4 + ----------                      
    1 + cos(x)
$$\log{\left (1 + \frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )} + \frac{4}{4 + \frac{4 \sin{\left (x \right )}}{\cos{\left (x \right )} + 1}}$$
Собрать выражение [src]
    /       /1 + cos(x) + sin(x)\\             /      sin(x)  \             /1 + cos(x) + sin(x)\
1 + |1 + log|-------------------||*cos(x) + log|1 + ----------|*sin(x) + log|-------------------|
    \       \     1 + cos(x)    //             \    1 + cos(x)/             \     1 + cos(x)    /
-------------------------------------------------------------------------------------------------
                                       1 + cos(x) + sin(x)
$$\frac{1}{\sin{\left (x \right )} + \cos{\left (x \right )} + 1} \left(\left(\log{\left (\frac{\sin{\left (x \right )} + \cos{\left (x \right )} + 1}{\cos{\left (x \right )} + 1} \right )} + 1\right) \cos{\left (x \right )} + \log{\left (\frac{\sin{\left (x \right )} + \cos{\left (x \right )} + 1}{\cos{\left (x \right )} + 1} \right )} + \log{\left (1 + \frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )} \sin{\left (x \right )} + 1\right)$$
                      /  sin(x)      \
                 4*log|---------- + 1|
      4               \1 + cos(x)    /
-------------- + ---------------------
     4*sin(x)              4          
4 + ----------                        
    1 + cos(x)
$$\frac{4}{4} \log{\left (1 + \frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )} + \frac{4}{4 + \frac{4 \sin{\left (x \right )}}{\cos{\left (x \right )} + 1}}$$
                                                         /    1          cos(x)       sin(x)  \               /    1          cos(x)       sin(x)  \        /    1          cos(x)       sin(x)  \       
                                                    4*log|---------- + ---------- + ----------|   4*cos(x)*log|---------- + ---------- + ----------|   4*log|---------- + ---------- + ----------|*sin(x)
           4                      4*cos(x)               \1 + cos(x)   1 + cos(x)   1 + cos(x)/               \1 + cos(x)   1 + cos(x)   1 + cos(x)/        \1 + cos(x)   1 + cos(x)   1 + cos(x)/       
----------------------- + ----------------------- + ------------------------------------------- + -------------------------------------------------- + --------------------------------------------------
4 + 4*cos(x) + 4*sin(x)   4 + 4*cos(x) + 4*sin(x)             4 + 4*cos(x) + 4*sin(x)                          4 + 4*cos(x) + 4*sin(x)                              4 + 4*cos(x) + 4*sin(x)
$$\frac{4 \sin{\left (x \right )}}{4 \sin{\left (x \right )} + 4 \cos{\left (x \right )} + 4} \log{\left (\frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} + \frac{\cos{\left (x \right )}}{\cos{\left (x \right )} + 1} + \frac{1}{\cos{\left (x \right )} + 1} \right )} + \frac{4 \cos{\left (x \right )}}{4 \sin{\left (x \right )} + 4 \cos{\left (x \right )} + 4} \log{\left (\frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} + \frac{\cos{\left (x \right )}}{\cos{\left (x \right )} + 1} + \frac{1}{\cos{\left (x \right )} + 1} \right )} + \frac{4}{4 \sin{\left (x \right )} + 4 \cos{\left (x \right )} + 4} \log{\left (\frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} + \frac{\cos{\left (x \right )}}{\cos{\left (x \right )} + 1} + \frac{1}{\cos{\left (x \right )} + 1} \right )} + \frac{4 \cos{\left (x \right )}}{4 \sin{\left (x \right )} + 4 \cos{\left (x \right )} + 4} + \frac{4}{4 \sin{\left (x \right )} + 4 \cos{\left (x \right )} + 4}$$
Комбинаторика [src]
              /      sin(x)  \      /      sin(x)  \                      /      sin(x)  \
1 + cos(x)*log|1 + ----------| + log|1 + ----------|*sin(x) + cos(x) + log|1 + ----------|
              \    1 + cos(x)/      \    1 + cos(x)/                      \    1 + cos(x)/
------------------------------------------------------------------------------------------
                                   1 + cos(x) + sin(x)
$$\frac{1}{\sin{\left (x \right )} + \cos{\left (x \right )} + 1} \left(\log{\left (1 + \frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )} \sin{\left (x \right )} + \log{\left (1 + \frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )} \cos{\left (x \right )} + \log{\left (1 + \frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )} + \cos{\left (x \right )} + 1\right)$$
Общий знаменатель [src]
           sin(x)            /      sin(x)  \
1 - ------------------- + log|1 + ----------|
    1 + cos(x) + sin(x)      \    1 + cos(x)/
$$\log{\left (1 + \frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )} + 1 - \frac{\sin{\left (x \right )}}{\sin{\left (x \right )} + \cos{\left (x \right )} + 1}$$
Тригонометрическая часть [src]
      4             /      sin(x)  \
-------------- + log|1 + ----------|
     4*sin(x)       \    1 + cos(x)/
4 + ----------                      
    1 + cos(x)
$$\log{\left (1 + \frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )} + \frac{4}{4 + \frac{4 \sin{\left (x \right )}}{\cos{\left (x \right )} + 1}}$$
Раскрыть выражение [src]
      4             /      sin(x)  \
-------------- + log|1 + ----------|
     4*sin(x)       \    1 + cos(x)/
4 + ----------                      
    1 + cos(x)
$$\log{\left (1 + \frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )} + \frac{4}{4 + \frac{4 \sin{\left (x \right )}}{\cos{\left (x \right )} + 1}}$$