(-sqrt(2)*atan(sqrt(3-2*x ... )))/(sqrt(3)) если x=-1/2 (упростите выражение)

Вы ввели

           /  _________\
   ___     |\/ 3 - 2*x |
-\/ 2 *atan|-----------|
           |  ___   ___|
           \\/ 2 *\/ x /
------------------------
           ___          
         \/ 3           

$$\frac{1}{\sqrt{3}} \left(-1 \sqrt{2} \operatorname{atan}{\left (\frac{1}{\sqrt{2} \sqrt{x}} \sqrt{- 2 x + 3} \right )}\right)$$

Подстановка условия

((-sqrt(2))*atan(sqrt(3 - 2*x)/(sqrt(2)*sqrt(x))))/sqrt(3) при x = -1/2

((-sqrt(2))*atan(sqrt(3 - 2*x)/(sqrt(2)*sqrt(x))))/sqrt(3)

$$\frac{1}{\sqrt{3}} \left(-1 \sqrt{2} \operatorname{atan}{\left (\frac{1}{\sqrt{2} \sqrt{x}} \sqrt{- 2 x + 3} \right )}\right)$$

((-sqrt(2))*atan(sqrt(3 - 2*(-1/2))/(sqrt(2)*sqrt((-1/2)))))/sqrt(3)

$$\frac{1}{\sqrt{3}} \left(-1 \sqrt{2} \operatorname{atan}{\left (\frac{1}{\sqrt{2} \sqrt{(-1/2)}} \sqrt{- 2 (-1/2) + 3} \right )}\right)$$

((-sqrt(2))*atan(sqrt(3 - 2*(-1)/2)/(sqrt(2)*sqrt(-1/2))))/sqrt(3)

$$\frac{1}{\sqrt{3}} \left(-1 \sqrt{2} \operatorname{atan}{\left (\frac{\sqrt{- -1 + 3}}{\sqrt{- \frac{1}{2}} \sqrt{2}} \right )}\right)$$

i*sqrt(6)*atanh(2)/3

$$\frac{\sqrt{6} i}{3} \operatorname{atanh}{\left (2 \right )}$$

Степени

           /  _________\ 
   ___     |\/ 6 - 4*x | 
-\/ 6 *atan|-----------| 
           |      ___  | 
           \  2*\/ x   / 
-------------------------
            3            

$$- \frac{\sqrt{6}}{3} \operatorname{atan}{\left (\frac{1}{2 \sqrt{x}} \sqrt{- 4 x + 6} \right )}$$

           /  ___   _________\ 
   ___     |\/ 2 *\/ 3 - 2*x | 
-\/ 6 *atan|-----------------| 
           |         ___     | 
           \     2*\/ x      / 
-------------------------------
               3               

$$- \frac{\sqrt{6}}{3} \operatorname{atan}{\left (\frac{\sqrt{2}}{2 \sqrt{x}} \sqrt{- 2 x + 3} \right )}$$

Численный ответ

-0.816496580927726*atan(sqrt(3 - 2*x)/(sqrt(2)*sqrt(x)))

Рациональный знаменатель

           /  ___   _________\ 
   ___     |\/ 2 *\/ 3 - 2*x | 
-\/ 6 *atan|-----------------| 
           |         ___     | 
           \     2*\/ x      / 
-------------------------------
               3               

$$- \frac{\sqrt{6}}{3} \operatorname{atan}{\left (\frac{\sqrt{2}}{2 \sqrt{x}} \sqrt{- 2 x + 3} \right )}$$

Объединение рациональных выражений

           /  ___   _________\ 
   ___     |\/ 2 *\/ 3 - 2*x | 
-\/ 6 *atan|-----------------| 
           |         ___     | 
           \     2*\/ x      / 
-------------------------------
               3               

$$- \frac{\sqrt{6}}{3} \operatorname{atan}{\left (\frac{\sqrt{2}}{2 \sqrt{x}} \sqrt{- 2 x + 3} \right )}$$

Общее упрощение

           /  ___   _________\ 
   ___     |\/ 2 *\/ 3 - 2*x | 
-\/ 6 *atan|-----------------| 
           |         ___     | 
           \     2*\/ x      / 
-------------------------------
               3               

$$- \frac{\sqrt{6}}{3} \operatorname{atan}{\left (\frac{\sqrt{2}}{2 \sqrt{x}} \sqrt{- 2 x + 3} \right )}$$

Собрать выражение

           /  _________\ 
   ___     |\/ 3 - 2*x | 
-\/ 6 *atan|-----------| 
           |  ___   ___| 
           \\/ 2 *\/ x / 
-------------------------
            3            

$$- \frac{\sqrt{6}}{3} \operatorname{atan}{\left (\frac{1}{\sqrt{2} \sqrt{x}} \sqrt{- 2 x + 3} \right )}$$

Комбинаторика

           /  ___   _________\ 
   ___     |\/ 2 *\/ 3 - 2*x | 
-\/ 6 *atan|-----------------| 
           |         ___     | 
           \     2*\/ x      / 
-------------------------------
               3               

$$- \frac{\sqrt{6}}{3} \operatorname{atan}{\left (\frac{\sqrt{2}}{2 \sqrt{x}} \sqrt{- 2 x + 3} \right )}$$

Общий знаменатель

           /  ___   _________\ 
   ___     |\/ 2 *\/ 3 - 2*x | 
-\/ 6 *atan|-----------------| 
           |         ___     | 
           \     2*\/ x      / 
-------------------------------
               3               

$$- \frac{\sqrt{6}}{3} \operatorname{atan}{\left (\frac{\sqrt{2}}{2 \sqrt{x}} \sqrt{- 2 x + 3} \right )}$$

Раскрыть выражение

         ___     /  ___   _________\
   ___ \/ 3      |\/ 2 *\/ 3 - 2*x |
-\/ 2 *-----*atan|-----------------|
         3       |         ___     |
                 \     2*\/ x      /

$$- \frac{\sqrt{6}}{3} \operatorname{atan}{\left (\frac{\sqrt{2}}{2 \sqrt{x}} \sqrt{- 2 x + 3} \right )}$$