6*sin(6*x)-4^acot(x)*log(4)/(1+x^2) если x=-1/3 (упростите выражение)

Вы ввели

              acot(x)       
             4       *log(4)
6*sin(6*x) - ---------------
                       2    
                  1 + x     

$$- \frac{4^{\operatorname{acot}{\left (x \right )}}}{x^{2} + 1} \log{\left (4 \right )} + 6 \sin{\left (6 x \right )}$$

Подстановка условия

6*sin(6*x) - 4^acot(x)*log(4)/(1 + x^2) при x = -1/3

6*sin(6*x) - 4^acot(x)*log(4)/(1 + x^2)

$$- \frac{4^{\operatorname{acot}{\left (x \right )}}}{x^{2} + 1} \log{\left (4 \right )} + 6 \sin{\left (6 x \right )}$$

6*sin(6*(-1/3)) - 4^acot((-1/3))*log(4)/(1 + (-1/3)^2)

$$- \frac{4^{\operatorname{acot}{\left ((-1/3) \right )}}}{(-1/3)^{2} + 1} \log{\left (4 \right )} + 6 \sin{\left (6 (-1/3) \right )}$$

6*sin(6*(-1)/3) - 4^acot(-1/3)*log(4)/(1 + (-1/3)^2)

$$6 \sin{\left (\frac{-6}{3} \right )} - \frac{\log{\left (4 \right )}}{4^{- \operatorname{acot}{\left (- \frac{1}{3} \right )}} \left(\left(- \frac{1}{3}\right)^{2} + 1\right)}$$

-6*sin(2) - 9*4^(-acot(1/3))*log(4)/10

$$- 6 \sin{\left (2 \right )} - \frac{9 \log{\left (4 \right )}}{10 \cdot 4^{\operatorname{acot}{\left (\frac{1}{3} \right )}}}$$

Степени

              2*acot(x)       
             2         *log(4)
6*sin(6*x) - -----------------
                        2     
                   1 + x      

$$- \frac{2^{2 \operatorname{acot}{\left (x \right )}}}{x^{2} + 1} \log{\left (4 \right )} + 6 \sin{\left (6 x \right )}$$

Численный ответ

6.0*sin(6*x) - 1.38629436111989*4.0^acot(x)/(1.0 + x^2)

Рациональный знаменатель

   acot(x)            /     2\         
- 4       *log(4) + 6*\1 + x /*sin(6*x)
---------------------------------------
                      2                
                 1 + x                 

$$\frac{1}{x^{2} + 1} \left(- 4^{\operatorname{acot}{\left (x \right )}} \log{\left (4 \right )} + 6 \left(x^{2} + 1\right) \sin{\left (6 x \right )}\right)$$

Объединение рациональных выражений

   acot(x)            /     2\         
- 4       *log(4) + 6*\1 + x /*sin(6*x)
---------------------------------------
                      2                
                 1 + x                 

$$\frac{1}{x^{2} + 1} \left(- 4^{\operatorname{acot}{\left (x \right )}} \log{\left (4 \right )} + 6 \left(x^{2} + 1\right) \sin{\left (6 x \right )}\right)$$

Общее упрощение

/       2\             acot(x)       
\6 + 6*x /*sin(6*x) - 4       *log(4)
-------------------------------------
                     2               
                1 + x                

$$\frac{1}{x^{2} + 1} \left(- 4^{\operatorname{acot}{\left (x \right )}} \log{\left (4 \right )} + \left(6 x^{2} + 6\right) \sin{\left (6 x \right )}\right)$$

Собрать выражение

/       2\             acot(x)       
\6 + 6*x /*sin(6*x) - 4       *log(4)
-------------------------------------
                     2               
                1 + x                

$$\frac{1}{x^{2} + 1} \left(- 4^{\operatorname{acot}{\left (x \right )}} \log{\left (4 \right )} + \left(6 x^{2} + 6\right) \sin{\left (6 x \right )}\right)$$

Общий знаменатель

                acot(x)       
             2*4       *log(2)
6*sin(6*x) - -----------------
                        2     
                   1 + x      

$$- \frac{2 \cdot 4^{\operatorname{acot}{\left (x \right )}}}{x^{2} + 1} \log{\left (2 \right )} + 6 \sin{\left (6 x \right )}$$

Комбинаторика

  /              acot(x)             2         \
2*\3*sin(6*x) - 4       *log(2) + 3*x *sin(6*x)/
------------------------------------------------
                          2                     
                     1 + x                      

$$\frac{1}{x^{2} + 1} \left(- 2 \cdot 4^{\operatorname{acot}{\left (x \right )}} \log{\left (2 \right )} + 6 x^{2} \sin{\left (6 x \right )} + 6 \sin{\left (6 x \right )}\right)$$

Раскрыть выражение

                                                                 acot(x)       
         3       3            5                   5             4       *log(4)
- 120*cos (x)*sin (x) + 36*cos (x)*sin(x) + 36*sin (x)*cos(x) - ---------------
                                                                          2    
                                                                     1 + x     

$$- \frac{4^{\operatorname{acot}{\left (x \right )}}}{x^{2} + 1} \log{\left (4 \right )} + 36 \sin^{5}{\left (x \right )} \cos{\left (x \right )} - 120 \sin^{3}{\left (x \right )} \cos^{3}{\left (x \right )} + 36 \sin{\left (x \right )} \cos^{5}{\left (x \right )}$$