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Общий знаменатель (-2*sqrt(3)*atan(sin(x)/( ... +2)+(cos(x)^2-4*cos(x))/2

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Примеры

Решение

Вы ввели [src]
                                                           2              
     ___     /      sin(x)      \                       cos (x) - 4*cos(x)
-2*\/ 3 *atan|------------------| + 3*log(cos(x) + 2) + ------------------
             |  ___             |                               2         
             \\/ 3 *(1 + cos(x))/
$$3 \log{\left (\cos{\left (x \right )} + 2 \right )} + - 2 \sqrt{3} \operatorname{atan}{\left (\frac{\sin{\left (x \right )}}{\sqrt{3} \left(\cos{\left (x \right )} + 1\right)} \right )} + \frac{1}{2} \left(\cos^{2}{\left (x \right )} - 4 \cos{\left (x \right )}\right)$$
Степени [src]
   2                                                 /   ___        \
cos (x)                                      ___     | \/ 3 *sin(x) |
------- - 2*cos(x) + 3*log(2 + cos(x)) - 2*\/ 3 *atan|--------------|
   2                                                 \3*(1 + cos(x))/
$$3 \log{\left (\cos{\left (x \right )} + 2 \right )} + \frac{1}{2} \cos^{2}{\left (x \right )} - 2 \cos{\left (x \right )} - 2 \sqrt{3} \operatorname{atan}{\left (\frac{\sqrt{3} \sin{\left (x \right )}}{3 \cos{\left (x \right )} + 3} \right )}$$
Численный ответ [src]
0.5*cos(x)^2 + 3.0*log(cos(x) + 2) - 2.0*cos(x) - 3.46410161513775*atan(sin(x)/(sqrt(3)*(1 + cos(x))))
Рациональный знаменатель [src]
                                                     /  ___       \
   2                                         ___     |\/ 3 *sin(x)|
cos (x) - 4*cos(x) + 6*log(2 + cos(x)) - 4*\/ 3 *atan|------------|
                                                     \3 + 3*cos(x)/
-------------------------------------------------------------------
                                 2
$$\frac{1}{2} \left(6 \log{\left (\cos{\left (x \right )} + 2 \right )} + \cos^{2}{\left (x \right )} - 4 \cos{\left (x \right )} - 4 \sqrt{3} \operatorname{atan}{\left (\frac{\sqrt{3} \sin{\left (x \right )}}{3 \cos{\left (x \right )} + 3} \right )}\right)$$
Объединение рациональных выражений [src]
                                                       /   ___        \
                                               ___     | \/ 3 *sin(x) |
6*log(2 + cos(x)) + (-4 + cos(x))*cos(x) - 4*\/ 3 *atan|--------------|
                                                       \3*(1 + cos(x))/
-----------------------------------------------------------------------
                                   2
$$\frac{1}{2} \left(\left(\cos{\left (x \right )} - 4\right) \cos{\left (x \right )} + 6 \log{\left (\cos{\left (x \right )} + 2 \right )} - 4 \sqrt{3} \operatorname{atan}{\left (\frac{\sqrt{3} \sin{\left (x \right )}}{3 \cos{\left (x \right )} + 3} \right )}\right)$$
Общее упрощение [src]
   2                                                 /   ___        \
cos (x)                                      ___     | \/ 3 *sin(x) |
------- - 2*cos(x) + 3*log(2 + cos(x)) - 2*\/ 3 *atan|--------------|
   2                                                 \3*(1 + cos(x))/
$$3 \log{\left (\cos{\left (x \right )} + 2 \right )} + \frac{1}{2} \cos^{2}{\left (x \right )} - 2 \cos{\left (x \right )} - 2 \sqrt{3} \operatorname{atan}{\left (\frac{\sqrt{3} \sin{\left (x \right )}}{3 \cos{\left (x \right )} + 3} \right )}$$
Собрать выражение [src]
   2                                                                        
cos (x)                  ___     /       sin(x)       \      /            3\
------- - 2*cos(x) - 2*\/ 3 *atan|--------------------| + log\(2 + cos(x)) /
   2                             |  ___     ___       |                     
                                 \\/ 3  + \/ 3 *cos(x)/
$$\log{\left (\left(\cos{\left (x \right )} + 2\right)^{3} \right )} + \frac{1}{2} \cos^{2}{\left (x \right )} - 2 \cos{\left (x \right )} - 2 \sqrt{3} \operatorname{atan}{\left (\frac{\sin{\left (x \right )}}{\sqrt{3} \cos{\left (x \right )} + \sqrt{3}} \right )}$$
1                                  cos(2*x)       ___     /       sin(x)       \
- - 2*cos(x) + 3*log(2 + cos(x)) + -------- - 2*\/ 3 *atan|--------------------|
4                                     4                   |  ___     ___       |
                                                          \\/ 3  + \/ 3 *cos(x)/
$$3 \log{\left (\cos{\left (x \right )} + 2 \right )} - 2 \cos{\left (x \right )} + \frac{1}{4} \cos{\left (2 x \right )} - 2 \sqrt{3} \operatorname{atan}{\left (\frac{\sin{\left (x \right )}}{\sqrt{3} \cos{\left (x \right )} + \sqrt{3}} \right )} + \frac{1}{4}$$
                                                           2              
                         ___     /      sin(x)      \   cos (x) - 4*cos(x)
3*log(cos(x) + 2) + -2*\/ 3 *atan|------------------| + ------------------
                                 |  ___             |           2         
                                 \\/ 3 *(1 + cos(x))/
$$\frac{1}{2} \left(\cos^{2}{\left (x \right )} - 4 \cos{\left (x \right )}\right) + 3 \log{\left (\cos{\left (x \right )} + 2 \right )} + - 2 \sqrt{3} \operatorname{atan}{\left (\frac{\sin{\left (x \right )}}{\sqrt{3} \left(\cos{\left (x \right )} + 1\right)} \right )}$$
Комбинаторика [src]
 /                                                       /   ___        \\ 
 |     2                                         ___     | \/ 3 *sin(x) || 
-|- cos (x) - 6*log(2 + cos(x)) + 4*cos(x) + 4*\/ 3 *atan|--------------|| 
 \                                                       \3*(1 + cos(x))// 
---------------------------------------------------------------------------
                                     2
$$- \frac{1}{2} \left(- 6 \log{\left (\cos{\left (x \right )} + 2 \right )} - \cos^{2}{\left (x \right )} + 4 \cos{\left (x \right )} + 4 \sqrt{3} \operatorname{atan}{\left (\frac{\sqrt{3} \sin{\left (x \right )}}{3 \cos{\left (x \right )} + 3} \right )}\right)$$
Общий знаменатель [src]
   2                                                 /   ___        \
cos (x)                                      ___     | \/ 3 *sin(x) |
------- - 2*cos(x) + 3*log(2 + cos(x)) - 2*\/ 3 *atan|--------------|
   2                                                 \3*(1 + cos(x))/
$$3 \log{\left (\cos{\left (x \right )} + 2 \right )} + \frac{1}{2} \cos^{2}{\left (x \right )} - 2 \cos{\left (x \right )} - 2 \sqrt{3} \operatorname{atan}{\left (\frac{\sqrt{3} \sin{\left (x \right )}}{3 \cos{\left (x \right )} + 3} \right )}$$
Тригонометрическая часть [src]
                    (-4 + cos(x))*cos(x)       ___     /      sin(x)      \
3*log(cos(x) + 2) + -------------------- - 2*\/ 3 *atan|------------------|
                             2                         |  ___             |
                                                       \\/ 3 *(1 + cos(x))/
$$\frac{1}{2} \left(\cos{\left (x \right )} - 4\right) \cos{\left (x \right )} + 3 \log{\left (\cos{\left (x \right )} + 2 \right )} - 2 \sqrt{3} \operatorname{atan}{\left (\frac{\sin{\left (x \right )}}{\sqrt{3} \left(\cos{\left (x \right )} + 1\right)} \right )}$$
Раскрыть выражение [src]
                       2                             /   ___        \
                    cos (x) - 4*cos(x)       ___     | \/ 3 *sin(x) |
3*log(cos(x) + 2) + ------------------ - 2*\/ 3 *atan|--------------|
                            2                        \3*(1 + cos(x))/
$$\frac{1}{2} \left(\cos^{2}{\left (x \right )} - 4 \cos{\left (x \right )}\right) + 3 \log{\left (\cos{\left (x \right )} + 2 \right )} - 2 \sqrt{3} \operatorname{atan}{\left (\frac{\sqrt{3} \sin{\left (x \right )}}{3 \cos{\left (x \right )} + 3} \right )}$$
   2                                                 /   ___        \
cos (x)                                      ___     | \/ 3 *sin(x) |
------- - 2*cos(x) + 3*log(2 + cos(x)) - 2*\/ 3 *atan|--------------|
   2                                                 \3*(1 + cos(x))/
$$3 \log{\left (\cos{\left (x \right )} + 2 \right )} + \frac{1}{2} \cos^{2}{\left (x \right )} - 2 \cos{\left (x \right )} - 2 \sqrt{3} \operatorname{atan}{\left (\frac{\sqrt{3} \sin{\left (x \right )}}{3 \cos{\left (x \right )} + 3} \right )}$$