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Общий знаменатель (3^sin(x)-atan(x^3))/sqrt ... *cos(x)*log(3))*acos(1-x)

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Примеры

Решение

Вы ввели [src]
 sin(x)       / 3\   /    2                         \            
3       - atan\x /   |-3*x      sin(x)              |            
------------------ + |------ + 3      *cos(x)*log(3)|*acos(1 - x)
   ______________    |     6                        |            
  /            2     \1 + x                         /            
\/  1 - (1 - x)
3sin⁡(x)−atan⁡(x3)−(−x+1)2+1+(−1⋅3x2x6+1+3sin⁡(x)cos⁡(x)log⁡(3))acos⁡(−x+1)\frac{3^{\sin{\left (x \right )}} - \operatorname{atan}{\left (x^{3} \right )}}{\sqrt{- \left(- x + 1\right)^{2} + 1}} + \left(\frac{-1 \cdot 3 x^{2}}{x^{6} + 1} + 3^{\sin{\left (x \right )}} \cos{\left (x \right )} \log{\left (3 \right )}\right) \operatorname{acos}{\left (- x + 1 \right )}
Степени [src]
 sin(x)       / 3\   /      2                         \            
3       - atan\x /   |   3*x      sin(x)              |            
------------------ + |- ------ + 3      *cos(x)*log(3)|*acos(1 - x)
   ______________    |       6                        |            
  /            2     \  1 + x                         /            
\/  1 - (1 - x)
3sin⁡(x)−atan⁡(x3)−(−x+1)2+1+(3sin⁡(x)log⁡(3)cos⁡(x)−3x2x6+1)acos⁡(−x+1)\frac{3^{\sin{\left (x \right )}} - \operatorname{atan}{\left (x^{3} \right )}}{\sqrt{- \left(- x + 1\right)^{2} + 1}} + \left(3^{\sin{\left (x \right )}} \log{\left (3 \right )} \cos{\left (x \right )} - \frac{3 x^{2}}{x^{6} + 1}\right) \operatorname{acos}{\left (- x + 1 \right )}
Численный ответ [src]
(1.0 - (1.0 - x)^2)^(-0.5)*(3.0^sin(x) - atan(x^3)) + (1.09861228866811*3.0^sin(x)*cos(x) - 3.0*x^2/(1.0 + x^6))*acos(1 - x)
Рациональный знаменатель [src]
   ____________                       ____________         ____________                          ____________           ______________    ____________                          ______________    ____________                                           ______________    ____________                          
  /    2            / 3\    sin(x)   /    2           6   /    2            / 3\    sin(x)  6   /    2             2   /            2    /    2                       sin(x)   /            2    /    2                                     sin(x)  6   /            2    /    2                                 
\/  - x  + 2*x *atan\x / - 3      *\/  - x  + 2*x  + x *\/  - x  + 2*x *atan\x / - 3      *x *\/  - x  + 2*x  + 3*x *\/  1 - (1 - x)  *\/  - x  + 2*x *acos(1 - x) - 3      *\/  1 - (1 - x)  *\/  - x  + 2*x *acos(1 - x)*cos(x)*log(3) - 3      *x *\/  1 - (1 - x)  *\/  - x  + 2*x *acos(1 - x)*cos(x)*log(3)
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                               /     6\ / 2      \                                                                                                                                               
                                                                                                                                               \1 + x /*\x  - 2*x/
1(x2−2x)(x6+1)(−3sin⁡(x)x6−x2+2x−(−x+1)2+1log⁡(3)cos⁡(x)acos⁡(−x+1)−3sin⁡(x)x6−x2+2x−3sin⁡(x)−x2+2x−(−x+1)2+1log⁡(3)cos⁡(x)acos⁡(−x+1)−3sin⁡(x)−x2+2x+x6−x2+2xatan⁡(x3)+3x2−x2+2x−(−x+1)2+1acos⁡(−x+1)+−x2+2xatan⁡(x3))\frac{1}{\left(x^{2} - 2 x\right) \left(x^{6} + 1\right)} \left(- 3^{\sin{\left (x \right )}} x^{6} \sqrt{- x^{2} + 2 x} \sqrt{- \left(- x + 1\right)^{2} + 1} \log{\left (3 \right )} \cos{\left (x \right )} \operatorname{acos}{\left (- x + 1 \right )} - 3^{\sin{\left (x \right )}} x^{6} \sqrt{- x^{2} + 2 x} - 3^{\sin{\left (x \right )}} \sqrt{- x^{2} + 2 x} \sqrt{- \left(- x + 1\right)^{2} + 1} \log{\left (3 \right )} \cos{\left (x \right )} \operatorname{acos}{\left (- x + 1 \right )} - 3^{\sin{\left (x \right )}} \sqrt{- x^{2} + 2 x} + x^{6} \sqrt{- x^{2} + 2 x} \operatorname{atan}{\left (x^{3} \right )} + 3 x^{2} \sqrt{- x^{2} + 2 x} \sqrt{- \left(- x + 1\right)^{2} + 1} \operatorname{acos}{\left (- x + 1 \right )} + \sqrt{- x^{2} + 2 x} \operatorname{atan}{\left (x^{3} \right )}\right)
Объединение рациональных выражений [src]
                                   ______________                                                      
/     6\ / sin(x)       / 3\\     /            2  /     2    sin(x) /     6\              \            
\1 + x /*\3       - atan\x // + \/  1 - (1 - x)  *\- 3*x  + 3      *\1 + x /*cos(x)*log(3)/*acos(1 - x)
-------------------------------------------------------------------------------------------------------
                                                   ______________                                      
                                       /     6\   /            2                                       
                                       \1 + x /*\/  1 - (1 - x)
1(x6+1)−(−x+1)2+1((3sin⁡(x)−atan⁡(x3))(x6+1)+(3sin⁡(x)(x6+1)log⁡(3)cos⁡(x)−3x2)−(−x+1)2+1acos⁡(−x+1))\frac{1}{\left(x^{6} + 1\right) \sqrt{- \left(- x + 1\right)^{2} + 1}} \left(\left(3^{\sin{\left (x \right )}} - \operatorname{atan}{\left (x^{3} \right )}\right) \left(x^{6} + 1\right) + \left(3^{\sin{\left (x \right )}} \left(x^{6} + 1\right) \log{\left (3 \right )} \cos{\left (x \right )} - 3 x^{2}\right) \sqrt{- \left(- x + 1\right)^{2} + 1} \operatorname{acos}{\left (- x + 1 \right )}\right)
Общее упрощение [src]
                                   ______________                                                      
/     6\ / sin(x)       / 3\\     /            2  /     2    sin(x) /     6\              \            
\1 + x /*\3       - atan\x // + \/  1 - (1 - x)  *\- 3*x  + 3      *\1 + x /*cos(x)*log(3)/*acos(1 - x)
-------------------------------------------------------------------------------------------------------
                                                   ______________                                      
                                       /     6\   /            2                                       
                                       \1 + x /*\/  1 - (1 - x)
1(x6+1)−(−x+1)2+1((3sin⁡(x)−atan⁡(x3))(x6+1)+(3sin⁡(x)(x6+1)log⁡(3)cos⁡(x)−3x2)−(−x+1)2+1acos⁡(−x+1))\frac{1}{\left(x^{6} + 1\right) \sqrt{- \left(- x + 1\right)^{2} + 1}} \left(\left(3^{\sin{\left (x \right )}} - \operatorname{atan}{\left (x^{3} \right )}\right) \left(x^{6} + 1\right) + \left(3^{\sin{\left (x \right )}} \left(x^{6} + 1\right) \log{\left (3 \right )} \cos{\left (x \right )} - 3 x^{2}\right) \sqrt{- \left(- x + 1\right)^{2} + 1} \operatorname{acos}{\left (- x + 1 \right )}\right)
Собрать выражение [src]
                                                  /   ______________                                           ______________                                  \                ______________                         
   sin(x) /      6\   /     6\     / 3\    sin(x) |  /            2                                       6   /            2                                   |           2   /            2                          
- 3      *\-1 - x / - \1 + x /*atan\x / - 3      *\\/  1 - (1 - x)  *(acos(-1 + x)*log(3) - pi*log(3)) + x *\/  1 - (1 - x)  *(acos(-1 + x)*log(3) - pi*log(3))/*cos(x) - x *\/  1 - (1 - x)  *(-3*acos(-1 + x) + 3*pi)
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                                                                                           ______________         ______________                                                                                       
                                                                                          /            2     6   /            2                                                                                        
                                                                                        \/  1 - (1 - x)   + x *\/  1 - (1 - x)
1x6−(−x+1)2+1+−(−x+1)2+1(−3sin⁡(x)(−x6−1)−3sin⁡(x)(x6(log⁡(3)acos⁡(x−1)−πlog⁡(3))−(−x+1)2+1+(log⁡(3)acos⁡(x−1)−πlog⁡(3))−(−x+1)2+1)cos⁡(x)−x2−(−x+1)2+1(−3acos⁡(x−1)+3π)−(x6+1)atan⁡(x3))\frac{1}{x^{6} \sqrt{- \left(- x + 1\right)^{2} + 1} + \sqrt{- \left(- x + 1\right)^{2} + 1}} \left(- 3^{\sin{\left (x \right )}} \left(- x^{6} - 1\right) - 3^{\sin{\left (x \right )}} \left(x^{6} \left(\log{\left (3 \right )} \operatorname{acos}{\left (x - 1 \right )} - \pi \log{\left (3 \right )}\right) \sqrt{- \left(- x + 1\right)^{2} + 1} + \left(\log{\left (3 \right )} \operatorname{acos}{\left (x - 1 \right )} - \pi \log{\left (3 \right )}\right) \sqrt{- \left(- x + 1\right)^{2} + 1}\right) \cos{\left (x \right )} - x^{2} \sqrt{- \left(- x + 1\right)^{2} + 1} \left(- 3 \operatorname{acos}{\left (x - 1 \right )} + 3 \pi\right) - \left(x^{6} + 1\right) \operatorname{atan}{\left (x^{3} \right )}\right)
     sin(x)               / 3\            2      2                    sin(x)                  sin(x)                                  sin(x)  6                  sin(x)  6                           
    3                 atan\x /      3*pi*x    3*x *acos(-1 + x)   pi*3      *cos(x)*log(3)   3      *acos(-1 + x)*cos(x)*log(3)   pi*3      *x *cos(x)*log(3)   3      *x *acos(-1 + x)*cos(x)*log(3)
--------------- - --------------- - ------- + ----------------- + ------------------------ - ---------------------------------- + --------------------------- - -------------------------------------
   ____________      ____________         6              6                      6                               6                                 6                                  6               
  /    2            /    2           1 + x          1 + x                  1 + x                           1 + x                             1 + x                              1 + x                
\/  - x  + 2*x    \/  - x  + 2*x
−3sin⁡(x)x6x6+1log⁡(3)cos⁡(x)acos⁡(x−1)+3sin⁡(x)πx6x6+1log⁡(3)cos⁡(x)−3sin⁡(x)x6+1log⁡(3)cos⁡(x)acos⁡(x−1)+3sin⁡(x)πx6+1log⁡(3)cos⁡(x)+3sin⁡(x)−x2+2x+3x2x6+1acos⁡(x−1)−3πx2x6+1−atan⁡(x3)−x2+2x- \frac{3^{\sin{\left (x \right )}} x^{6}}{x^{6} + 1} \log{\left (3 \right )} \cos{\left (x \right )} \operatorname{acos}{\left (x - 1 \right )} + \frac{3^{\sin{\left (x \right )}} \pi x^{6}}{x^{6} + 1} \log{\left (3 \right )} \cos{\left (x \right )} - \frac{3^{\sin{\left (x \right )}}}{x^{6} + 1} \log{\left (3 \right )} \cos{\left (x \right )} \operatorname{acos}{\left (x - 1 \right )} + \frac{3^{\sin{\left (x \right )}} \pi}{x^{6} + 1} \log{\left (3 \right )} \cos{\left (x \right )} + \frac{3^{\sin{\left (x \right )}}}{\sqrt{- x^{2} + 2 x}} + \frac{3 x^{2}}{x^{6} + 1} \operatorname{acos}{\left (x - 1 \right )} - \frac{3 \pi x^{2}}{x^{6} + 1} - \frac{\operatorname{atan}{\left (x^{3} \right )}}{\sqrt{- x^{2} + 2 x}}
Комбинаторика [src]
                                                        ____________                          ____________                                           ____________                          
 sin(x)       / 3\    sin(x)  6    6     / 3\      2   /    2                       sin(x)   /    2                                     sin(x)  6   /    2                                 
3       - atan\x / + 3      *x  - x *atan\x / - 3*x *\/  - x  + 2*x *acos(1 - x) + 3      *\/  - x  + 2*x *acos(1 - x)*cos(x)*log(3) + 3      *x *\/  - x  + 2*x *acos(1 - x)*cos(x)*log(3)
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                                                                             _____________ /     2\ /     4    2\                                                                          
                                                                           \/ -x*(-2 + x) *\1 + x /*\1 + x  - x /
1−x(x−2)(x2+1)(x4−x2+1)(3sin⁡(x)x6−x2+2xlog⁡(3)cos⁡(x)acos⁡(−x+1)+3sin⁡(x)x6+3sin⁡(x)−x2+2xlog⁡(3)cos⁡(x)acos⁡(−x+1)+3sin⁡(x)−x6atan⁡(x3)−3x2−x2+2xacos⁡(−x+1)−atan⁡(x3))\frac{1}{\sqrt{- x \left(x - 2\right)} \left(x^{2} + 1\right) \left(x^{4} - x^{2} + 1\right)} \left(3^{\sin{\left (x \right )}} x^{6} \sqrt{- x^{2} + 2 x} \log{\left (3 \right )} \cos{\left (x \right )} \operatorname{acos}{\left (- x + 1 \right )} + 3^{\sin{\left (x \right )}} x^{6} + 3^{\sin{\left (x \right )}} \sqrt{- x^{2} + 2 x} \log{\left (3 \right )} \cos{\left (x \right )} \operatorname{acos}{\left (- x + 1 \right )} + 3^{\sin{\left (x \right )}} - x^{6} \operatorname{atan}{\left (x^{3} \right )} - 3 x^{2} \sqrt{- x^{2} + 2 x} \operatorname{acos}{\left (- x + 1 \right )} - \operatorname{atan}{\left (x^{3} \right )}\right)
Общий знаменатель [src]
                                                        ____________                                                
 sin(x)       / 3\    sin(x)  6    6     / 3\      2   /    2                                                       
3       - atan\x / + 3      *x  - x *atan\x / - 3*x *\/  - x  + 2*x *acos(1 - x)    sin(x)                          
-------------------------------------------------------------------------------- + 3      *acos(1 - x)*cos(x)*log(3)
                         ____________         ____________                                                          
                        /    2           6   /    2                                                                 
                      \/  - x  + 2*x  + x *\/  - x  + 2*x
3sin⁡(x)log⁡(3)cos⁡(x)acos⁡(−x+1)+1x6−x2+2x+−x2+2x(3sin⁡(x)x6+3sin⁡(x)−x6atan⁡(x3)−3x2−x2+2xacos⁡(−x+1)−atan⁡(x3))3^{\sin{\left (x \right )}} \log{\left (3 \right )} \cos{\left (x \right )} \operatorname{acos}{\left (- x + 1 \right )} + \frac{1}{x^{6} \sqrt{- x^{2} + 2 x} + \sqrt{- x^{2} + 2 x}} \left(3^{\sin{\left (x \right )}} x^{6} + 3^{\sin{\left (x \right )}} - x^{6} \operatorname{atan}{\left (x^{3} \right )} - 3 x^{2} \sqrt{- x^{2} + 2 x} \operatorname{acos}{\left (- x + 1 \right )} - \operatorname{atan}{\left (x^{3} \right )}\right)
Тригонометрическая часть [src]
 sin(x)       / 3\   /    2                         \            
3       - atan\x /   |-3*x      sin(x)              |            
------------------ + |------ + 3      *cos(x)*log(3)|*acos(1 - x)
   ______________    |     6                        |            
  /            2     \1 + x                         /            
\/  1 - (1 - x)
3sin⁡(x)−atan⁡(x3)−(−x+1)2+1+(3sin⁡(x)log⁡(3)cos⁡(x)+−1⋅3x2x6+1)acos⁡(−x+1)\frac{3^{\sin{\left (x \right )}} - \operatorname{atan}{\left (x^{3} \right )}}{\sqrt{- \left(- x + 1\right)^{2} + 1}} + \left(3^{\sin{\left (x \right )}} \log{\left (3 \right )} \cos{\left (x \right )} + \frac{-1 \cdot 3 x^{2}}{x^{6} + 1}\right) \operatorname{acos}{\left (- x + 1 \right )}
Раскрыть выражение [src]
 sin(x)       / 3\                       /      2                         \
3       - atan\x /                       |   3*x      sin(x)              |
------------------ + (pi - acos(-1 + x))*|- ------ + 3      *cos(x)*log(3)|
   ______________                        |       6                        |
  /            2                         \  1 + x                         /
\/  1 - (1 - x)
3sin⁡(x)−atan⁡(x3)−(−x+1)2+1+(3sin⁡(x)log⁡(3)cos⁡(x)−3x2x6+1)(−acos⁡(x−1)+π)\frac{3^{\sin{\left (x \right )}} - \operatorname{atan}{\left (x^{3} \right )}}{\sqrt{- \left(- x + 1\right)^{2} + 1}} + \left(3^{\sin{\left (x \right )}} \log{\left (3 \right )} \cos{\left (x \right )} - \frac{3 x^{2}}{x^{6} + 1}\right) \left(- \operatorname{acos}{\left (x - 1 \right )} + \pi\right)